Waves · Physics · MHT CET

Two sound waves having frequencies 250 Hz and 256 Hz superimpose to produce beat wave. The resultant beat wave has intensity maximum at $\mathrm{t}=0$. After how much time an intensity will be minimum produced at the same point?

A pipe 60 cm long and open at both the ends produces harmonics. Which harmonic mode of pipe resonates a 2.2 KHz source? (Speed of sound in air $=330 \mathrm{~m} / \mathrm{s})($ Neglect end correction)

A source and listener are both moving towards each other with speed $\frac{\mathrm{V}}{10}$. (where V is speed of sound) If the frequency of sound note emitted by the source is ' $n$ ', then the frequency heard by the listener would be nearly

Two uniform strings A and B made of steel are made to vibrate under the same tension. If first overtone of A is equal to the second overtone of $B$ and if the radius of $A$ is twice that of $B$, the ratio of the length of string $B$ to that of $A$ is

A string is under tension of 180 N and mass per unit length $2 \times 10^{-3} \mathrm{Kg} / \mathrm{m}$. It produces two consecutive resonant frequencies with a tuning fork, which are 375 Hz and 450 Hz . The mass of the string is

How many times more intense is a 60 dB sound that a 30 dB sound?

The end correction for the vibrations of air column in a tube of circular cross-section will be more if the tube is

A wave is given by $Y=3 \sin 2 \pi\left(\frac{t}{0.04}-\frac{x}{0.01}\right)$ where Y is in cm . Frequency of the wave and maximum acceleration will be $\left(\pi^2=10\right)$

Velocity of sound waves in air is $330 \mathrm{~m} / \mathrm{s}$. For a particular sound wave in air, path difference of 40 cm is equivalent to phase difference of $1.6 \pi$. frequency of this wave is

A string has mass per unit length of $10^{-6} \mathrm{~kg} / \mathrm{cm}$ The equation of simple harmonic wave produced in it is $\mathrm{Y}=0.2 \sin (2 \mathrm{x}+80 \mathrm{t}) \mathrm{m}$. The tension in the string is

The driver of a car travelling with a speed ' $V_1$ ' $\mathrm{m} / \mathrm{s}$ towards a wall sounds a siren of frequency ' $n$ ' Hz. If the velocity of sound in air is $\mathrm{V} \mathrm{m} / \mathrm{s}$, then the frequency of sound reflected from the wall and as heard by the driver, in Hz , is

An open organ pipe of length ' $l$ ' is sounded together with another open organ pipe of length $\left(l+l_1\right)$ in their fundamental modes. Speed of sound in air is ' $V$ '. The beat frequency heard will be ( $\left.l_1< < l\right)$

Two progressive waves $Y_1=\sin 2 \pi\left(\frac{t}{0 \cdot 4}-\frac{x}{4}\right)$ and $Y_2=\sin 2 \pi\left(\frac{t}{0 \cdot 4}+\frac{x}{4}\right)$ superpose to form a standing wave. ' $x$ ' and ' $y$ ' are in SI system. Amplitude of the particle at $x=0.5 \mathrm{~m}$ is $\left[\sin 45^{\circ}=\cos 45^{\circ}=\frac{1}{\sqrt{2}}\right]$

When a sonometer wire vibrates in third overtone there are

Which of the following statements is NOT true?

If the two waves of same amplitude, having frequencies 340 Hz and 335 Hz , are moving in same direction, then the time interval between two successive maxima formed (in second) is

The frequency of the third overtone of a pipe of length ' $L_{\mathrm{c}}$ ', closed at one end is same as the frequency of the sixth overtone of a pipe of length ' $L_0$ ', open at both ends. Then the ratio $\mathrm{L}_{\mathrm{c}}: \mathrm{L}_0$ is

A wire of length ' $L$ ' and linear density ' $m$ ' is stretched between two rigid supports with tension ' $T$ '. It is observed that wire resonates in the $\mathrm{P}^{\text {th }}$ harmonic at a frequency of 320 Hz and resonates again at next higher frequency of 400 Hz . The value of ' $p$ ' is

The frequency of two tuning forks A and B are respectively $1.4 \%$ more and $2.6 \%$ less than that of the tuning fork C . When A and B are sounded together, 10 beats are produced in 1 second. The frequency of tuning fork C is

A resonance tube closed at one end is of height 1.5 m . A tuning fork of frequency 340 Hz is vibrating above the tube. Water is poured in the tube gradually. The minimum height of water column for which resonance is obtained is (Neglect end correction, speed of sound in air $=340 \mathrm{~m} / \mathrm{s}$ )

At the poles of earth, a stretched wire of a given length vibrates in unison with a tuning fork. At the equator of earth, for same setting, to produce resonance with same fork, the vibrating length of wire

With what velocity an observer should move relative to a stationary source so that a sound of triple the frequency of source is heard by an observer?

The length of a sonometer wire 'AB' is 110 cm . Where should the two bridges be placed from end ' $A$ ' to divide the wire in three segments whose fundamental frequencies are in the ratio $1: 2: 3$ ?

Prong of a vibrating tuning fork is in contact with water surface. It produces concentric circular waves on the surface of water. The distance between five consecutive crests is 0.8 m and the velocity of wave on the water surface is $56 \mathrm{~m} / \mathrm{s}$. The frequency of tuning fork is

The end correction for the vibrations of air column in a tube of circular cross-section will be more if the tube is

Stationary wave is produced along the stretched string of length 80 cm . The resonant frequencies of string are $90 \mathrm{~Hz}, 150 \mathrm{~Hz}$ and 210 Hz . The speed of transverse wave in the string is

The pipe open at both ends and pipe closed at one end have same length and both are vibrating in fundamental mode. Air column vibrating in open pipe has resonance frequency $n_1$ and air column vibrating in closed pipe has resonance frequency $\mathrm{n}_2$, then

Two sound waves having displacements $x_1=2 \sin (1000 \pi t)$ and $x_2=3 \sin (1006 \pi t)$, when interfere, produce

When the listener moves towards stationary source with velocity ' $\mathrm{V}_1$ ', the apparent frequency of emitted note is ' $F_1$ '. When observer moves away from the source with velocity ' $\mathrm{V}_1$ ', apparent frequency is ' $F_2$ '. If V is the velocity of sound in air and $\frac{F_1}{F_2}=2$ then $\frac{V}{V_1}$ is

When the string is stretched between two rigid supports, under certain tension and vibrated

A musical instrument X produces sound waves of frequency n and amplitude A. Another musical instrument $Y$ produces sound waves of frequency $\frac{n}{3}$. The waves produced by $x$ and $y$ have equal energies. The amplitude of waves produced by Y will be

A stationary wave is formed having 3 nodes along the length of the string 90 cm . The wavelength of the wave is

The diagram shows the propagation of a progressive wave. A, B, C, D, E are five points on this wave

Which of the following points are in the same state of vibration?

A string of mass 0.2 Kg is under a tension of 2.5 N . The length of the string is 2 m. A transverse wave starts from one end of the string. The time taken by the wave to reach the other end is

A musical instrument ' $P$ ' produces sound waves of frequency ' $n$ ' and amplitude ' $A$ '. Another musical instrument ' $Q$ ' produces sound waves of frequency $\frac{\mathrm{n}}{4}$. The waves produced by ' $P$ ' and ' $Q$ ' have equal energies. If the amplitude of waves produced by ' $P$ ' is ' $A_P$ ', the amplitude of waves produced by ' $Q$ ' will be

A sonometer wire is in unison with a tuning fork of frequency ' $n$ ' when it is stretched by a weight of specific gravity ' $d$ '. When the weight is completely immersed in water, ' $x$ ' beats are produced per second, then

The equations of two waves are given as

$$\begin{aligned} & y_1=a \sin \left(\omega t+\phi_1\right) \\ & y_2=a \sin \left(\omega t+\phi_2\right) \end{aligned}$$

If amplitude and time period of resultant wave is same as the individual waves, then $\left(\phi_1-\phi_2\right)$ is

Two sound waves having same amplitude ' $A$ ' and angular frequency ' $\omega$ ' but having a phase difference of $\left(\frac{\pi}{2}\right)^c$ are superimposed then the maximum amplitude of the resultant wave is

Out of the following musical instruments, which is 'NOT' a percussion instrument?

When the tension in string is increased by $3 \mathrm{~kg} \omega \mathrm{t}$, the frequency of the fundamental mode increases in the ratio $2: 3$. The initial tension in the string is

A sonometer wire is stretched by hanging a metal bob, the fundamental frequency of the wire is ' $n_1$ '. When the bob is completely immersed in water, the frequency of vibration of wire becomes ' $n_2$ '. The relative density of the metal of the bob is

A tuning fork of frequency 340 Hz is vibrated just above a tube of 120 cm height. Water is slowly poured in the tube. What is the minimum height of water necessary for resonance?

A stationery wave is represented by $y=12 \cos \left(\frac{\pi}{6} x\right) \sin (8 \pi t)$, where $x \& y$ are in cm and $t$ in second. The distance between two successive antinodes is

A transverse wave travelling along a stretched string has a speed of $30 \mathrm{~m} / \mathrm{s}$ and a frequency of 250 Hz . The phase difference between two points on the string 10 cm apart at the same instant is

A train sounding a whistle of frequency 510 Hz approaches a station at $72 \mathrm{~km} / \mathrm{hr}$. The frequency of the note heard by an observer on the platform as the train (1) approaches the station and then (2) recedes the station are respectively (in hertz) (velocity of sound in air $=320 \mathrm{~m} / \mathrm{s}$ )

A set of 28 turning forks is arranged in an increasing order of frequencies. Each fork produces ' $x$ ' beats per second with the preceding fork and the last fork is an octave of the first. If the frequency of the $12^{\text {th }}$ fork is 152 Hz , the value of ' $x$ ' (no. of beats per second) is

Two waves $\mathrm{Y}_1=0.25 \sin 316 \mathrm{t} \quad$ and $\mathrm{Y}_2=0.25 \sin 310 \mathrm{t}$ are propagating along the same direction. The number of beats produced per second are

The distance between two consecutive points with phase difference of $60^{\circ}$ in wave of frequency 500 Hz is 0.6 m . The velocity with which wave is travelling is

A string A has twice the length, twice the diameter, twice the tension and twice the density of another string B. The overtone of A which will have the same fundamental frequency as that of $B$ is

A progressive wave of frequency 400 Hz is travelling with a velocity $336 \mathrm{~m} / \mathrm{s}$. How far apart are the two points which are $60^{\circ}$ out of phase?

The end correction of resonance tube is 1 cm. If the shortest length resonating with a tuning fork is 15 cm , the next resonating length will be

If ' $l$ ' is the length of pipe, ' $r$ ' is the internal radius of the pipe and ' $v$ ' is the velocity of sound in air then fundamental frequency of open pipe is

A violin emits sound waves of frequency ' $n_1$ ' under tension T. When tension is increased by $44 \%$, keeping the length and mass per unit length constant, frequency of sound waves becomes ' $\mathrm{n}_2$ '. The ratio of frequency ' $\mathrm{n}_2$ ' to frequency ' $n_1$ ' is

An observer moves towards a stationary source of sound with a velocity of one-fifth of the velocity of sound. The percentage increase in the apparent frequency is

The path difference between two waves $\mathrm{Y}_1=\mathrm{a}_1 \sin \left(\omega \mathrm{t}-\frac{2 \pi \mathrm{x}}{\lambda}\right)$ and $\mathrm{Y}_2=\mathrm{a}_2 \cos \left(\omega \mathrm{t}-\frac{2 \pi \mathrm{x}}{\lambda}+\phi\right)$ is

The fundamental frequency of an air column in a pipe open at both ends is ' $\mathrm{f}_1$ '. Now $80 \%$ of its length is immersed in water, the fundamental frequency of the air column becomes $f_2$. The ratio of $f_1: f_2$ is

The pitch of a whistle of an engine appears to drop by $30 \%$ of original value when it passes a stationary observer. If the speed of sound in air is $350 \mathrm{~ms}^{-1}$, then the speed of engine in $\mathrm{ms}^{-1}$ is

The displacement of a wave is given by $y=0.002 \sin (100 t+x)$ where ' $x$ 'and ' $y$ ' are in metre and ' $t$ ' is in second. This represents a wave

In a vibrating string with fixed ends the waves are of type

The driver of a car travelling with a speed ' $V_1$ ' $\mathrm{m} / \mathrm{s}$ towards a wall sounds a siren of frequency ' $n$ ' Hz. If the velocity of sound in air is ' V ' $\mathrm{m} / \mathrm{s}$, then the frequency of the sound reflected from the wall and as heard by the driver in Hz is

A stretched string is fixed at both ends. It is made to vibrate so that the total number of nodes formed in it is ' $x$ '. The length of the string in terms of the wavelength of waves formed in it is ( $\lambda=$ wavelength $)$

A sonometer wire is stretched by hanging a metal bob. The fundamental frequency of vibration of wire is ' $n_1$ '. When the bob is completely immersed in water, the frequency of vibration of wire becomes ' $n_2$ '. The relative density of the metal of the bob is

Two simple harmonic progressive waves have displacements $\rightarrow \mathrm{y}_1=\mathrm{a}_1 \sin \left(\frac{2 \pi \mathrm{x}}{\lambda}-\omega \mathrm{t}\right)$ and $\mathrm{y}_2=\mathrm{a}_2 \cos \left(\frac{2 \pi \mathrm{x}}{\lambda}-\omega \mathrm{t}+\phi\right)$ What is the phase difference between two waves?

A wire under tension 225 N produces 6 beats per second when it is tuned with a fork. When the tension changes to 256 N , it is again tuned with the same tuning fork, the number of beats remain unchanged. The frequency of tuning fork will be

Velocity of sound waves in air is $330 \mathrm{~m} / \mathrm{s}$. For a particular sound wave in air, path difference of 40 cm is equivalent to phase difference of $1.6 \pi$. The frequency of this wave is

An air column in a closed organ pipe vibrating in unison with a fork, produces second overtone. The vibrating air column has

Sound waves of frequency $$600 \mathrm{~Hz}$$ fall normally on a perfectly reflecting wall. The shortest distance from the wall at which all particles will have maximum amplitude of vibration is (speed of sound $$=300 \mathrm{~ms}^{-1}$$ )

A wire $$P Q$$ has length $$4.8 \mathrm{~m}$$ and mass $$0.06 \mathrm{~kg}$$. Another wire QR has length $$2.56 \mathrm{~m}$$ and mass $$0.2 \mathrm{~kg}$$. Both wires have same radii and are joined as a single wire. This wire is under tension of $$80 \mathrm{~N}$$. A wave pulse of amplitude $$3.5 \mathrm{~cm}$$ is sent along the wire $$\mathrm{PQ}$$ from end $$\mathrm{P}$$. the time taken by the wave pulse to travel along the wire from point P to R is ?

A sonometer wire $$49 \mathrm{~cm}$$ long is in unison with a tuning fork of frequency '$$n$$'. If the length of the wire is decreased by $$1 \mathrm{~cm}$$ and it is vibrated with the same tuning fork, 6 beats are heard per second. The value of '$$n$$' is

A source of sound is moving towards a stationary observer with $$\left(\frac{1}{10}\right)^{\text {th }}$$ the of the speed of sound. The ratio of apparent to real frequency is

A string is stretched between two rigid supports separated by $$75 \mathrm{~cm}$$. There are no resonant frequencies between $$420 \mathrm{~Hz}$$ and $$315 \mathrm{~Hz}$$. The lowest resonant frequency for the string is

A progressive wave is given by, $$\mathrm{Y}=12 \sin (5 \mathrm{t}-4 \mathrm{x})$$. On this wave, how far away are the two points having a phase difference of $$90^{\circ}$$ ?

The equation of the wave is $$\mathrm{Y}=10 \sin \left(\frac{2 \pi \mathrm{t}}{30}+\alpha\right)$$ If the displacement is $$5 \mathrm{~cm}$$ at $$\mathrm{t}=0$$ then the total phase at $$\mathrm{t}=7.5 \mathrm{~s}$$ will be $$\left(\sin 30^{\circ}=0.5\right)$$

If '$$l$$' is the length of the open pipe, '$$r$$' is the internal radius of the pipe and '$V$ ' is the velocity of sound in air then fundamental frequency of open pipe is

When two tuning forks are sounded together, 5 beats per second are heard. One of the forks is in unison with $$0.97 \mathrm{~m}$$ length of sonometer wire and the other is in unison with $$0.96 \mathrm{~m}$$ length of the same wire. The frequencies of the two tuning forks are

The equation of a progressive wave is $$Y=a \sin 2 \pi\left(n t-\frac{x}{5}\right)$$. The ratio of maximum particle velocity to wave velocity is

A transverse wave strike against a wall,

A closed pipe and an open pipe have their first overtone equal in frequency. Then, the lengths of these pipe are in the ratio

In resonance tube, first and second resonance are obtained at depths $$22.7 \mathrm{~cm}$$ and $$70.2 \mathrm{~cm}$$ respectively. The third resonance will be obtained at a depth

A uniform wire $$20 \mathrm{~m}$$ long and weighing $$50 \mathrm{~N}$$ hangs vertically. The speed of the wave at mid point of the wire is (acceleration due to gravity $$=\mathrm{g}=10 \mathrm{~ms}^{-2}$$ )

A passenger is sitting in a train which is moving fast. The engine of the train blows a whistle of frequency '$$n$$'. If the apparent frequency of sound heard by the passenger is '$$f$$' then

The equation of wave motion is $$Y=5 \sin (10 \pi t -0.02 \pi x+\pi / 3)$$ where $$x$$ is in metre and $$t$$ in second. The velocity of the wave is

End correction at open end for air column in a pipe of length '$$l$$' is '$$e$$'. For its second overtone of an open pipe, the wavelength of the wave is

A tuning fork gives 3 beats with $$50 \mathrm{~cm}$$ length of sonometer wire. If the length of the wire is shortened by $$1 \mathrm{~cm}$$, the number of beats is still the same. The frequency of the fork is

A tuning fork of frequency $$220 \mathrm{~Hz}$$ produces sound waves of wavelength $$1.5 \mathrm{~m}$$ in air at N.T.P. The increase in wavelength when the temperature of air is $$27^{\circ} \mathrm{C}$$ is nearly $$\left(\sqrt{\frac{300}{273}}=1.05\right)$$

A uniform string is vibrating with a fundamental frequency '$$n$$'. If radius and length of string both are doubled keeping tension constant then the new frequency of vibration is

The displacement of two sinusoidal waves is given by the equation

$$\begin{aligned} & \mathrm{y}_1=8 \sin (20 \mathrm{x}-30 \mathrm{t}) \\ & \mathrm{y}_2=8 \sin (25 \mathrm{x}-40 \mathrm{t}) \end{aligned}$$

then the phase difference between the waves after time $$t=2 \mathrm{~s}$$ and distance $$x=5 \mathrm{~cm}$$ will be

Two sounding sources send waves at certain temperature in air of wavelength $$50 \mathrm{~cm}$$ and $$50.5 \mathrm{~cm}$$ respectively. The frequency of sources differ by $$6 \mathrm{~Hz}$$. The velocity of sound in air at same temperature is

41 tuning forks are arranged in increasing order of frequency such that each produces 5 beats/second with next tuning fork. If frequency of last tuning fork is double that of frequency of first fork. Then frequency of first and last fork is

A transverse wave in a medium is given by $$y=A \sin 2(\omega t-k x)$$. It is found that the magnitude of the maximum velocity of particles in the medium is equal to that of the wave velocity. What is the value of $$A$$ ?

A rectangular block of mass '$$\mathrm{m}$$' and crosssectional area A, floats on a liquid of density '$$\rho$$'. It is given a small vertical displacement from equilibrium, it starts oscillating with frequency '$$n$$' equal to ( $$g=$$ acceleration due to gravity)

A sound of frequency $$480 \mathrm{~Hz}$$ is emitted from the stringed instrument. The velocity of sound in air is $$320 \mathrm{~m} / \mathrm{s}$$. After completing 180 vibrations, the distance covered by a wave is

A sonometer wire '$$A$$' of diameter '$$\mathrm{d}$$' under tension '$$T$$' having density '$$\rho_1$$' vibrates with fundamental frequency '$$n$$'. If we use another wire '$$B$$' which vibrates with same frequency under tension '$$2 \mathrm{~T}$$' and diameter '$$2 \mathrm{D}$$' then density '$$\rho_2$$' of wire '$$B$$' will be

The path difference between two waves, represented by $$\mathrm{y}_1=\mathrm{a}_1 \sin \left(\omega \mathrm{t}-\frac{2 \pi \mathrm{x}}{\lambda}\right)$$ and $$y_2=a_2 \cos \left(\omega t-\frac{2 \pi x}{\lambda}+\phi\right)$$ is

Two progressive waves are travelling towards each other with velocity $$50 \mathrm{~m} / \mathrm{s}$$ and frequency $$200 \mathrm{~Hz}$$. The distance between the two consecutive antinodes is

A string fixed at both the ends forms standing wave with node separation of $$5 \mathrm{~cm}$$. If the velocity of the wave on the string is $$2 \mathrm{~m} / \mathrm{s}$$, then the frequency of vibration of the string is

The second overtone of an open pipe has the same frequency as the first overtone of a closed pipe of length '$$L$$'. The length of the open pipe will be

A car sounding a horn of frequency $$1000 \mathrm{~Hz}$$ passes a stationary observer. The ratio of frequencies of the horn noted by the observer before and after passing the car is $$11: 9$$. If the speed of sound is '$$v$$', the speed of the car is

A transverse wave $$\mathrm{Y}=2 \sin (0.01 \mathrm{x}+30 \mathrm{t})$$ moves on a stretched string from one end to another end in 0.5 second. If $$x$$ and $$y$$ are in $$\mathrm{cm}$$ and $$t$$ in second, then the length of the string is

The fundamental frequency of air column in pipe 'A' closed at one end is in unison with second overtone of an air column in pipe 'B' open at both ends. The ratio of length of air column in pipe '$$\mathrm{A}$$' to that of air column in pipe '$$\mathrm{B}$$' is

The equation of wave is $$Y=6 \sin$$ $$\left(12 \pi t-0.02 \pi x+\frac{\pi}{3}\right)$$ where '$$x$$' is in $$m$$ and '$$t$$' in $$\mathrm{s}$$. The velocity of the wave is

Two uniform wires of same material are vibrating under the same tension. If the first overtone of first wire is equal to the $$2^{\text {nd }}$$ overtone of $$2^{\text {nd }}$$ wire and radius of the first wire is twice the radius of the $$2^{\text {nd }}$$ wire then the ratio of length of first wire to $$2^{\text {nd }}$$ wire is

A uniform rope of length '$$L$$' and mass '$$m_1$$' hangs vertically from a rigid support. A block of mass '$$m_2$$' is attached to the free end of the rope. A transverse wave of wavelength '$$\lambda_1$$' is produced at the lower end of the rope. The wavelength of the wave when it reaches the top of the rope is '$$\lambda_2$$'. The ratio $$\frac{\lambda_1}{\lambda_2}$$ is

An open organ pipe having fundamental frequency (n) is in unison with a vibrating string. If the tube is dipped in water so that $$75 \%$$ of the length of the tube is inside the water then the ratio of fundamental frequency of the air column of dipped tube with that of string will be (Neglect end corrections)

In case of a stationary wave pattern which of the following statement is CORRECT?

If the length of stretched string is reduced by $$40 \%$$ and tension is increased by $$44 \%$$ then the ratio of final to initial frequencies of stretched string is

Consider the Doppler effect in two cases. In the first case, an observer moves towards a stationary source of sound with a speed of $$50 \mathrm{~m} / \mathrm{s}$$. In the second case, the observer is at rest and the source moves towards the observer with the same speed of $$50 \mathrm{~m} / \mathrm{s}$$. Then the frequency heard by the observer will be

[velocity of sound in air $$=330 \mathrm{~m} / \mathrm{s}$$.]

The equation of simple harmonic progressive wave is given by $$y=a \sin 2 \pi(b t-c x)$$. The maximum particle velocity will be half the wave velocity, if $$\mathrm{c}=$$

Stationary waves can be produced in

If the length of an open organ pipe is $$33.3 \mathrm{~cm}$$, then the frequency of fifth overtone is [Neglect end correction, velocity of sound $$=333 \mathrm{~m} / \mathrm{s}$$ ]

If the end correction of an open pipe is $$0.8 \mathrm{~cm}$$, then the inner radius of that pipe is

When both source and listener are approaching each other the observed frequency of sound is given by $$\left(V_L\right.$$ and $$V_S$$ is the velocity of listener and source respectively, $$\mathrm{n}_0=$$ radiated frequency)

Equation of simple harmonic progressive wave is given by $$y=\frac{1}{\sqrt{a}} \sin \omega t \pm \frac{1}{\sqrt{b}} \cos \omega t$$ then the resultant amplitude of the wave is $$\left(\cos 90^{\circ}=0\right)$$

When a string of length '$$l$$' is divided into three segments of length $$l_1, l_2$$ and $$l_3$$. The fundamental frequencies of three segments are $$\mathrm{n}_1, \mathrm{n}_2$$ and $$\mathrm{n}_3$$ respectively. The original fundamental frequency '$$n$$' of the string is

A closed organ pipe of length '$$L_1$$' and an open organ pipe contain diatomic gases of densities '$$\rho_1$$' and '$$\rho_2$$' respectively. The compressibilities of the gases are same in both pipes, which are vibrating in their first overtone with same frequency. The length of the open organ pipe is (Neglect end correction)

A stationary wave is represented by $$\mathrm{y}=10 \sin \left(\frac{\pi \mathrm{x}}{4}\right) \cos (20 \pi \mathrm{t})$$ where $$\mathrm{x}$$ and $$\mathrm{y}$$ are in $$\mathrm{cm}$$ and $$\mathrm{t}$$ in second. The distance between two consecutive nodes is

Two waves are superimposed whose ratio of intensities is $$9: 1$$. The ratio of maximum and minimum intensity is

Consider the following statements about stationary waves.

A. The distance between two adjacent nodes or antinodes is equal to $$\frac{\lambda}{2}(\lambda=$$ wavelength of the wave)

B. A node is always formed at the open end of the open organ pipe.

Choose the correct option from the following.

A hollow pipe of length $$0.8 \mathrm{~m}$$ is closed at one end. At its open end, a $$0.5 \mathrm{~m}$$ long uniform string is vibrating in its second harmonic and it resonates with the fundamental frequency of pipe. If the tension in the string is $$50 \mathrm{~N}$$ and speed of sound in air is $$320 \mathrm{~m} / \mathrm{s}$$, the mass of the string is

A cylindrical tube open at both ends has fundamental frequency 'n' in air. The tube is dipped vertically in water so that one-fourth of it is in water. The fundamental frequency of the air column becomes

Velocity of sound waves in air is '$$\mathrm{V}$$' $$\mathrm{m} / \mathrm{s}$$. For a particular sound wave in air, path difference of 'x' $$\mathrm{cm}$$ is equivalent to phase difference $$n \pi$$. The frequency of this wave is

The length and diameter of a metal wire used in sonometer is doubled. The fundamental frequency will change from 'n' to

A closed organ pipe and an open organ pipe of same length produce 2 beats per second when they are set into vibrations together in fundamental mode. The length of open pipe is now halved and that of closed pipe is doubled. The number of beats produced per second will be

A sonometer wire of length 25 cm vibrates in unison with a tuning fork. When its length is decreased by 1 cm, 6 beats are heard per second. What is the frequency of the tuning fork?

Two tuning forks of frequencies $$320 \mathrm{~Hz}$$ and $$480 \mathrm{~Hz}$$ are sounded together to produce sound waves. The velocity of sound in air is $$320 \mathrm{~ms}^{-1}$$. The difference between wavelengths of these waves is nearly

When an air column in a pipe open at both ends vibrates such that four antinodes and three nodes are formed, then the corresponding mode of vibration is

The wavelength of sound in any gas depends upon

A uniform rope of length $$12 \mathrm{~m}$$ and mass $$6 \mathrm{~kg}$$ hangs vertically from the rigid support. A block of mass $$2 \mathrm{~kg}$$ is attached to the free end of the rope. A transverse pulse of wavelength $$0.06 \mathrm{~m}$$ is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is

What is the effect of pressure on the speed of sound in a medium, if pressure is doubled at constant temperature?

Two sound waves having wavelengths $$5.0 \mathrm{~m}$$ and $$5.5 \mathrm{~m}$$ propagates in a gas with velocity 300 $$\mathrm{m} / \mathrm{s}$$. The number of heats produced per second is

The frequency of a tuning fork is $$220 \mathrm{~Hz}$$ and the velocity of sound in air is $$330 \mathrm{~m} / \mathrm{s}$$. When the tuning fork completes 80 vibrations, the distance travelled by the

Two waves $$\mathrm{Y}_1=0.25 \sin 316 \mathrm{t}$$ and $$\mathrm{Y}_2=0.25 \sin 310 \mathrm{t}$$ are propagation same direction. The number of beats produced per second are

Two waves are represented by the equation, $$\mathrm{y}_1=\mathrm{A} \sin (\omega \mathrm{t}+\mathrm{kx}+0.57) \mathrm{m}$$ and $$\mathrm{y}_2=\mathrm{A} \cos (\omega \mathrm{t}+\mathrm{kx}) \mathrm{m}$$, where $$\mathrm{x}$$ is in metre and $$\mathrm{t}$$ is in second. What is the phase difference between them?

The fundamental frequency of an air column in pipe 'A' closed at one end coincides with second overtone of pipe 'B' open at both ends. The ratio of length of pipe 'A' to that of pipe 'B' is

A tuning fork of frequency '$$n$$' is held near the open end of tube which is closed at the other end and the lengths are adjusted until resonance occurs. The first resonance occurs at length $$L_1$$ and immediate next resonance occurs at length $$L_2$$. The speed of sound in air is

A sound wave of frequency $$160 \mathrm{~Hz}$$ has a velocity of $$320 \mathrm{~m} / \mathrm{s}$$. When it travels through air, the particles having a phase difference of $$90^{\circ}$$, are separated by a distance of

A glass tube of $$1 \mathrm{~m}$$ length is filled with water. The water can be drained out slowly from the bottom of the tube. If vibrating tuning fork of frequency $$500 \mathrm{~Hz}$$ is brought at the upper end of the tube then total number of resonances obtained are [Velocity of sound in air is $$320 \mathrm{~ms}^{-1}$$]

A sound wave is travelling with a frequency of $$50 \mathrm{~Hz}$$. The phase difference between the two points in the path of a wave is $$\frac{\pi}{3}$$. The distance between those two points is (Velocity of sound in air $$=330 \mathrm{~m} / \mathrm{s}$$ )

A transverse wave given by $$y=2 \sin (0.01 x+30 t)$$ moves on a stretched string from one end to another end in 0.5 second. If '$$x$$' and '$$y$$' are in $$\mathrm{cm}$$ and '$$\mathrm{t}$$' is in second, then the length of the string is

A pipe open at both ends of length 1.5 m is dipped in water such that the second overtone of vibrating air column is resonating with a tuning fork of frequency 330 Hz. If speed of sound in air is 330 m/s then the length of the pipe immersed in water is (Neglect and correction)

A sonometer wire resonates with a given tuning fork forming standing waves with five antinodes between the two bridges when a mass of $$9 \mathrm{~kg}$$ is suspended from the wire. When this mass is replaced by a mass $$\mathrm{M}$$, the wire resonates with the same tuning fork forming three antinodes for the same positions of the bridges. The value of '$$M$$' is

Equation of two simple harmonic waves are given by $${Y_1} = 2\sin 8\pi \left( {{t \over {0.2}} - {x \over 2}} \right)m$$ and $${Y_2} = 4\sin 8\pi \left( {{t \over {0.16}} - {x \over {1.6}}} \right)m$$ then both waves have

A pipe closed at one end has length $$0.8 \mathrm{~m}$$. At its open end $$0.5 \mathrm{~m}$$ long uniform string is vibrating in its $$2^{\text {nd }}$$ harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the wire is $$50 \mathrm{~N}$$ and the speed of sound is $$320 \mathrm{~m} / \mathrm{s}$$, the mass of the string is

The equation of simple harmonic wave produced in the string under tension $$0.4 \mathrm{~N}$$ is given by $$\mathrm{y=4 \sin (3 x+60 t) ~m}$$. The mass per unit length of the string is

A closed organ pipe of length '$$\mathrm{L}_c$$' and an open organ pipe of length '$$\mathrm{L}_{\mathrm{o}}$$' contain different gases of densities '$$\rho_1$$' and '$$\rho_2$$' respectively. The compressibility of the gases is the same in both the pipes. The gases are vibrating in their first overtone with the same frequency. What is the length of open organ pipe?

A progressive wave of frequency 50 Hz is travelling with velocity 350 m/s through a medium. The change in phase at a given time interval of 0.01 second is

A simple harmonic progressive wave is given by $$Y=Y_0 \sin 2 \pi\left(n t-\frac{x}{\lambda}\right)$$. If the wave velocity is $$\left(\frac{1}{8}\right)^{\text {th }}$$ the maximum particle velocity then the wavelength is

In fundamental mode, the time required for the sound wave to reach upto the closed end of pipe filled with air is $$t$$ second. The frequency of vibration of air column is

Which one of the following statements is true?

Two consecutive harmonics of an air column in a pipe closed at one end are of frequencies 150 Hz and 250 Hz. The fundamental frequency of an air column is

An air column in a pipe, which is closed at one end will be in resonance with a vibrating tuning fork of frequency 264 Hz for various lengths. Which one of the following lengths is not possible? (V = 330 m/s)

Beats are produced by waves $$\mathrm{y_1=a\sin2000\pi t}$$ and $$\mathrm{y_2=a\sin2008\pi t}$$. The number of beats heard per second is

The frequencies of three tuning forks $$\mathrm{A}, \mathrm{B}$$ and $$\mathrm{C}$$ are related as $$\mathrm{n}_{\mathrm{A}}>\mathrm{n}_{\mathrm{B}}>\mathrm{n}_{\mathrm{C}}$$. When the forks $$\mathrm{A}$$ and $$\mathrm{B}$$ are sounded together, the number of beats produced per second is '$$n_1$$'. When forks $$\mathrm{A}$$ and $$\mathrm{C}$$ are sounded together the number of beats produced per second is '$$n_2$$'. How may beats are produced per second when forks $$\mathrm{B}$$ and $$\mathrm{C}$$ are sounded together?

The equation of wave is given by $$\mathrm{y}=10 \sin \left(\frac{2 \pi \mathrm{t}}{30}+\alpha\right)$$. If the displacement is $$5 \mathrm{~cm}$$ at $$\mathrm{t}=0$$, then the total phase at $$\mathrm{t}=7.5 \mathrm{~s}$$ will be

$$\left[\sin 30^{\circ}=\cos 60^{\circ}=\frac{1}{2}, \cos 30^{\circ}=\sin 60^{\circ}=\frac{\sqrt{3}}{2}\right] $$

A sonometer wire resonates with 4 antinodes between two bridges for a given tuning fork, when 1 kg mass is suspended from the wire. Using same fork, when mass M is suspended, the wire resonates producing 2 antinodes between the two bridges (distance between two bridges is as before). The value of M is

Two wires of same material of radius 'r' and '2r' respectively are welded together end to end. The combination is then used as a sonometer wire under tension 'T'. The joint is kept midway between the two bridges. The ratio of the number of loops formed in the wires such that the joint is a node is

The frequency of a tuning fork is 'n' Hz and velocity of sound in air is 'V' m/s. When the tuning fork completes 'x' vibrations, the distance travelled by the wave is

A tuning fork $A$ produces 5 beats per second with a tuning fork of frequency 480 Hz . When a little wax is stuck to a prong of fork $A$, the number of beats heard per second becomes 2 . What is the frequency of tuning fork $A$ before the wax is stuck to it ?

At the poles, a stretched wire of a given length vibrates in unison with a tuning fork. At the equator, for same setting to produce resonance with same fork, the vibrating length of wire

A uniform metal wire has length $L$, mass $M$ and density $\rho$. It is under tension $T$ and $v$ is the speed of transverse wave along the wire. The area of cross-section of the wire is

The fundamental frequency of a closed pipe is 400 Hz . If $\frac{1}{3}$ rd pipe is filled with water, then the frequency of 2nd harmonic of the pipe will be (neglect and correction)

A sonometer wire under suitable tension having specific gravity $$\rho$$, vibrates with frequency $$n$$ in air. If the load is completely immersed in water the frequency of vibration of wire will become

An obstacle is moving towards the source with velocity $$v$$. The sound is reflected from the obstacle. If $$c$$ is the speed of sound and $$\lambda$$ is the wavelength, then the wavelength of the reflected wave $$\lambda_r$$ is

An open organ pipe and a closed organ pipe have the frequency of their first overtone identical. The ratio of length of open pipe to that of closed pipe is

When tension $$T$$ is applied to a sonometer wire of length $$I$$, it vibrates with the fundamental frequency $$n$$. Keeping the experimental setup same, when the tension is increased by 8 N, the fundamental frequency becomes three times the earlier fundamental frequency $$n$$. The initial tension applied to the wire (in newton) was

The extension in a wire obeying Hooke's law is $$x$$. The speed of sound in the stretched wire is $$v$$. If the extension in the wire is increased to $$4 x$$, then the speed of sound in a wire is

Two waves $$Y_1=0.25 \sin 316 t$$ and $$Y_2=0.25 \sin 310 t$$ are propagating along the same direction. The number of beats produced per second are

Two identical strings of length $$l$$ and $$2l$$ vibrate with fundamental frequencies $$\mathrm{N} \mathrm{~Hz}$$ and $$1.5 N$$ Hz, respectively. The ratio of tensions for smaller length to large length is

When open pipe is closed from one end third overtone of closed pipe is higher in frequency by $$150 \mathrm{~Hz}$$, then second overtone of open pipe. The fundamental frequency of open end pipe will be

A pipe open at both ends and a pipe closed at one end have same length. The ratio of frequencies of their $P^{\text {th }}$ overtone is

The fundamental frequency of sonometer wire increases by 9 Hz , if its tension is increased by $69 \%$, keeping the length constant. The frequency of the wire is

A sonometer wire is in unison with a tuning fork, when it is stretched by weight $w$ and the corresponding resonating length is $L_4$. If the weight is reduced to $\left(\frac{w}{4}\right)$, the corresponding resonating length becomes $L_2$. The ratio $\left(\frac{L_1}{L_2}\right)$ is

For formation of beats, two sound notes must have

A stretched string fixed at both ends has ' $m$ ' nodes, then the length of the string will be

A stretched wire of length 260 cm is set into vibrations. It is divided into three segments whose frequencies are in the ratio $2: 3: 4$. Their lengths must be

A simple harmonic progressive wave is represented as $y=0.03 \sin \pi(2 t-0.01 x) \mathrm{m}$. At a given instant of time, the phase difference between two particles 25 m apart is

Find the wrong statement from the following about the equation of stationary wave given by $Y=0.04 \cos (\pi x) \sin (50 \pi t) \mathrm{m}$ where $t$ is in second. Then for the stationary wave.

Two open pipes of different lengths and same diameter in which the air column vibrates with fundamental frequencies ' $n_1$ ', and ' $n_2$ ' respectively. When both pipes are joined to form a single pipe, its fundamental frequency will be

The equation of simple harmonic progressive wave is given by $Y=a \sin 2 \pi(b t-c x)$. The maximum particle velocity will be twice the wave velocity if

In a fundamental mode,the time required for the sound wave to reach upto the closed end of a pipe filled with air is ' $t$ ' second. The frequency of vibration of air column is

A transverse wave is propagating on the string. The linear density of a vibrating string is $10^{-3} \mathrm{~kg} / \mathrm{m}$. The equation of the wave is $Y=0.05 \sin (x+15 t)$ where $x$ and $Y$ are measured in metre and time in second. The tension force in the string is