## MCQ (Single Correct Answer)

A steel wire with mass per unit length $$7.0 \times 10^{-3} \mathrm{~kg} \mathrm{~m}^{-1}$$ is under tension of $$70 \mathrm{~N}$$. The speed of trans...

A person observes two moving trains, 'A' reaching the station and 'B' leaving the station with equal speed of $$30 \mathrm{~m} / \mathrm{s}$$. If both...

A travelling wave is described by the equation
$$y(x,t) = [0.05\sin (8x - 4t)]$$ m
The velocity of the wave is : [all the quantities are in SI unit]...

In the wave equation
$$
y=0.5 \sin \frac{2 \pi}{\lambda}(400 \mathrm{t}-x) \,\mathrm{m}
$$
the velocity of the wave will be:

A transverse wave is represented by $$y=2 \sin (\omega t-k x)\, \mathrm{cm}$$. The value of wavelength (in $$\mathrm{cm}$$) for which the wave velocit...

Which of the following equations correctly represents a travelling wave having wavelength $$\lambda$$ = 4.0 cm, frequency v = 100 Hz and travelling in...

A longitudinal wave is represented by $$x = 10\sin 2\pi \left( {nt - {x \over \lambda }} \right)$$ cm. The maximum particle velocity will be four time...

The velocity of sound in a gas, in which two wavelengths 4.08 m and 4.16 m produce 40 beats in 12s, will be :

If a wave gets refracted into a denser medium, then which of the following is true?

An observer moves towards a stationary source of sound with a velocity equal to one-fifth of the velocity of sound. The percentage change in the frequ...

For a specific wavelength 670 nm of light coming from a galaxy moving with velocity v, the observed wavelength is 670.7 nm. The value of v is :

Two massless springs with spring constants 2 k and 9 k, carry 50 g and 100 g masses at their free ends. These two masses oscillate vertically such tha...

The equations of two waves are given by :
y1 = 5 sin 2$$\pi$$(x - vt) cm
y2 = 3 sin 2$$\pi$$(x $$-$$ vt + 1.5) cm
These waves are simultaneously passi...

The motion of a mass on a spring, with spring constant K is as shown in figure.The equation of motion is given by x(t) = A sin$$\omega$$t + B cos$$\om...

A sound wave of frequency 245 Hz travels with the speed of 300 ms$$-$$1 along the positive x-axis. Each point of the wave moves to and from through a ...

For what value of displacement the kinetic energy and potential energy of a simple harmonic oscillation become equal ?

A tuning fork A of unknown frequency produces 5 beats/s with a fork of known frequency 340 Hz. When fork A is field, the beat frequency decreases to 2...

A student is performing the experiment of resonance column. The diameter of the column tube is 6 cm. The frequency of the tuning fork is 504 Hz. Speed...

Which of the following equations represents a travelling wave?

In the given figure, a mass M is attached to a horizontal spring which is fixed on one side to a rigid support. The spring constant of the spring is k...

A sound source S is moving along a straight track with speed v, and is emitting, sound of frequency
v0
(see figure). An observer is standing at a fin...

A driver in a car, approaching a vertical wall
notices that the frequency of his car horn, has
changed from 440 Hz to 480 Hz, when it gets
reflected f...

Two coherent sources of sound, S1 and S2,
produce sound waves of the same wavelength,
$$\lambda $$ = 1 m, in phase. S1 and S2 are placed 1.5 m
apart (...

The driver of a bus approaching a big wall notices that the frequency of his bus's horn changes
from 420 Hz to 490 Hz when he hears it after it gets r...

For a transverse wave travelling along a straight line, the distance between two peaks (crests) is 5 m, while the distance between one crest and one t...

A uniform thin rope of length 12 m and mass 6 kg hangs vertically from a rigid support and a block
of mass 2 kg is attached to its free end. A transve...

An amplitude modulated wave is represented
by the expression vm = 5(1 + 0.6 cos 6280t)
sin(211 × 104 t) volts
The minimum and maximum amplitudes of th...

Three harmonic waves having equal frequency
$$\nu $$ and same intensity $${I_0}$$, have phase angles 0, $${\pi \over 4}$$ and $$ - {\pi \over 4}$$ r...

A transverse wave travels on a taut steel wire
with a velocity of v when tension in it is
2.06 × 104 N. When the tension is changed to
T, the velocity...

A stationary observer receives sound from two identical tuning forks, one of which approaches
and the other one recedes with the same speed (much less...

Speed of a transverse wave on a straight wire (mass 6.0 g, length 60 cm and area of cross-section 1.0 mm2) is 90 ms-1. If the Young's modulus of wire ...

Two sources of sound S1 and S2 produce sound waves of same frequency 660 Hz. A listener is moving from
source S1 towards S2 with a constant speed u m/...

A tuning fork of frequency 480 Hz is used in an experiment for measuring speed of sound (v) in air
by resonance tube method. Resonance is observed to ...

A small speaker delivers 2 W of audio output. At what distance from the speaker will one detect 120 dB
intensity sound ? [Given reference intensity of...

A progressive wave travelling along the positive x-direction is represented by y(x,t) = Asin(kx – $$\omega $$t + $$\phi $$). Its
snapshot at t = 0 is ...

A submarine (A) travelling at 18 km/hr is being chased along the line of its velocity by another submarine
(B) travelling at 27 km/hr. B sends a sonar...

The correct figure that shows, schematically, the wave pattern produced by superposition of two waves of
frequencies 9 Hz and 11 Hz, is :

A source of sound S is moving with a velocity of 50 m/s towards a stationary observer. The observer
measures the frequency of the source as 1000 Hz. W...

The displacement of a damped harmonic
oscillator is given by
x(t ) = e–0.1t cos (10$$\pi $$t + f). Here t is in seconds.
The time taken for its amplit...

A stationary source emits sound waves of
frequency 500 Hz. Two observers moving
along a line passing through the source detect
sound to be of frequenc...

Two cars A and B are moving away from each
other in opposite directions. Both the cars are
moving with a speed of 20 ms–1 with respect
to the ground. ...

A string 2.0 m long and fixed at its ends is
driven by a 240 Hz vibrator. The string vibrates
in its third harmonic mode. The speed of the
wave and it...

The pressure wave, P = 0.01 sin [1000t – 3x] Nm–2,
corresponds to the sound produced by a vibrating blade
on a day when atmospheric temperature is 0°C...

A string is clamped at both the ends and it is
vibrating in its 4th harmonic. The equation of the
stationary wave is Y = 0.3 sin(0.157x) cos(200pt).
T...

A damped harmonic oscillator has a frequency
of 5 oscillations per second. The amplitude
drops to half its value for every 10 oscillations.
The time i...

A wire of length 2L, is made by joining two
wires A and B of same length but different radii
r and 2r and made of the same material. It is
vibrating ...

A resonance tube is old and has jagged end. It is still used in the laboratory to determine velocity of sound in air. A tuning fork of frequency 512 H...

Equation of travelling wave on a stretched string of linear density 5 g/m is y = 0.03 sin(450 t – 9x) where distance and time are measured in SI units...

A train moves towards a stationary observer with speed 34 m/s. The train sounds a whistle and its frequency registered by the observer is ƒ1. If the s...

In an electron microscope, the resolution that can be achieved is of the order of the wavelength of electrons used. To resolve a width of 7.5 × 10–12 ...

A string of length 1 m and mass 5 g is fixed at both ends. The tension in the string is 8.0 N. The string is set into vibration using an external vibr...

A rod of mass 'M' and length '2L' is suspended at its middle by a wire. It exhibits torsional oscillations; If two masses each of 'm' are attached at ...

A musician using an open flute of length 50 cm producess second harmonic sound waves. A person runs towards the musician from another end of hall at ...

Two coherent sources produce waves of different intensities which interfere. After interference, the ratio of the maximum intensity to the minimum int...

Two sitar strings, A and B, playing the note 'Dha' are slightly out of tune and produce beats of frequency 5 Hz. The tension of the string B s slight...

The end correction of a resonance column is 1 cm. If the shortest length resonating with the tunning fork is 10 cm, the next resonating length should...

A silver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of 1012/sec. What is the force constant of the bonds ...

A granite rod of 60 cm length is clamped at its middle point and is set into longitudinal vibrations. The
density of granite is 2.7 $$\times$$ 103 kg/...

5 beats / econd are heard when a tuning fork is sounded with a sonometer wire under tension, when the length of the sonometer wire is either 0.95 m or...

A tuning fork vibrates with frequency $$256$$ $$Hz$$ and gives one beat per second with the third normal mode of vibration of an open pipe. What is th...

A standing wave is formed by the superposition of two waves travelling in
opposite directions. The transverse displacement is given by
y(x, t) = 0.5 s...

In an experiment to determine the period of a simple pendulum of length 1 m, it is attached to different spherical bobs of radii r1
and r2 . The two ...

Two wires W1 and W2 have the same radius r and respective densities $$\rho $$1 and $$\rho $$2 such that ρ2 = 4$$\rho $$1 . They are joined together...

A particle is executing simple harmonic motion with a time period T. At time t = 0, it is at its position of
equilibrium. The kinetic energy – time gr...

A toy-car, blowing its horn, is moving with a steady speed of 5 m/s, away from a wall. An observer, towards whom the toy car is moving, is able to hea...

Two engines pass each other moving in opposite directions with uniform speed of 30 m/s. One of them is blowing a whistle of frequency 540 Hz. Calculat...

A uniform string of length $$20$$ $$m$$ is suspended from a rigid support. A short wave pulse is introduced at its lowest end. It starts moving up the...

A pipe open at both ends has a fundamental frequency $$f$$ in air. The pipe is dipped vertically in water so that half of it is in water. The fundamen...

A train is moving on a straight track with speed $$20\,m{s^{ - 1}}.$$ It is blowing its whistle at the frequency of $$1000$$ $$Hz$$. The percentage ch...

A pipe of length $$85$$ $$cm$$ is closed from one end. Find the number of possible natural oscillations of air column in the pipe whose frequencies li...

A sonometer wire of length $$1.5$$ $$m$$ is made of steel. The tension in it produces an elastic strain of $$1\% $$. What is the fundamental frequenc...

A cylindrical tube, open at both ends, has a fundamental frequency, $$f,$$ in air. The tube is dipped vertically in water so that half of it is in wat...

The transverse displacement $$y(x, t)$$ of a wave on a string is given by $$y\left( {x,t} \right) = {e^{ - \left( {a{x^2} + b{t^2} + 2\sqrt {ab} \,xt}...

The equation of a wave on a string of linear mass density $$0.04\,\,kg\,{m^{ - 1}}$$ is given by
$$$y = 0.02\left( m \right)\,\sin \left[ {2\pi \left...

Three sound waves of equal amplitudes have frequencies $$\left( {v - 1} \right),\,v,\,\left( {v + 1} \right).$$ They superpose to give beats. The numb...

A motor cycle starts from rest and accelerates along a straight path at $$2m/{s^2}.$$ At the starting point of the motor cycle there is a stationary e...

While measuring the speed of sound by performing a resonance column experiment, a student gets the first resonance condition at a column length of $$1...

A wave travelling along the $$x$$-axis is described by the equation $$y(x, t)=0.005$$ $$\cos \,\left( {\alpha \,x - \beta t} \right).$$ If the wavelen...

A sound absorber attenuates the sound level by $$20$$ $$dB$$. The intensity decreases by a factor of

A whistle producing sound waves of frequencies $$9500$$ $$Hz$$ and above is approaching a stationary person with speed $$v$$ $$m{s^{ - 1}}.$$ The velo...

A string is stretched between fixed points separated by $$75.0$$ $$cm.$$ It is observed to have resonant frequencies of $$420$$ $$Hz$$ and $$315$$ $$H...

When two tuning forks (fork $$1$$ and fork $$2$$) are sounded simultaneously, $$4$$ beats per second are heated. Now, some tape is attached on the pro...

An observer moves towards a stationary source of sound, with a velocity one-fifth of the velocity of sound. What is the percentage increase in the app...

The displacement $$y$$ of a particle in a medium can be expressed as, $$y = {10^{ - 6}}\,\sin $$ $$\left( {100t + 20x + {\pi \over 4}} \right)$$ $$m$...

A metal wire of linear mass density of $$9.8$$ $$g/m$$ is stretched with a tension of $$10$$ $$kg$$-$$wt$$ between two rigid supports $$1$$ metre apar...

The displacement $$y$$ of a wave travelling in the $$x$$-direction is given by
$$$y = {10^{ - 4}}\,\sin \left( {600t - 2x + {\pi \over 3}} \right)\,...

A tuning fork of known frequency $$256$$ $$Hz$$ makes $$5$$ beats per second with the vibrating string of a piano. The beat frequency decreases to $$2...

length of a string tied to two rigid supports is $$40$$ $$cm$$. Maximum length (wavelength in $$cm$$) of a stationary wave produced on it is

A tuning fork arrangement (pair) produces $$4$$ beats/sec with one fork of frequency $$288$$ $$cps.$$ A little wax is placed on the unknown fork and i...

Tube $$A$$ has bolt ends open while tube $$B$$ has one end closed, otherwise they are identical. The ratio of fundamental frequency of tube $$A$$ and ...

A wave $$y=a$$ $$\sin \left( {\omega t - kx} \right)$$ on a string meets with another wave producing a node at $$x=0.$$ Then the equation of the unkno...

When temperature increases, the frequency of a tuning fork

## Numerical

The displacement equations of two interfering waves are given by
$y_{1}=10 \sin \left(\omega t+\frac{\pi}{3}\right) \mathrm{cm}, y_{2}=5[\sin \omega ...

Two simple harmonic waves having equal amplitudes of 8 cm and equal frequency of 10 Hz are moving along the same direction. The resultant amplitude is...

A train blowing a whistle of frequency 320 Hz approaches an observer standing on the platform at a speed of 66 m/s. The frequency observed by the obse...

The distance between two consecutive points with phase difference of 60$$^\circ$$ in a wave of frequency 500 Hz is 6.0 m. The velocity with which wave...

The frequency of echo will be __________ Hz if the train blowing a whistle of frequency 320 Hz is moving with a velocity of 36 km/h towards a hill fro...

A wire of length 30 cm, stretched between rigid supports, has it's nth and (n + 1)th harmonics at 400 Hz and 450 Hz, respectively. If tension in the s...

When a car is approaching the observer, the frequency of horn is $$100 \mathrm{~Hz}$$. After passing the observer, it is $$50 \mathrm{~Hz}$$. If the o...

Two waves executing simple harmonic motions travelling in the same direction with same amplitude and frequency are superimposed. The resultant amplitu...

An observer is riding on a bicycle and moving towards a hill at $$18 \,\mathrm{kmh}^{-1}$$. He hears a sound from a source at some distance behind him...

An employee of a factory moving away from his workplace by a car listens to the siren of the factory. He drives the car at the speed of 72 kmh$$-$$1 i...

In an experiment to determine the velocity of sound in air at room temperature using a resonance tube, the first resonance is observed when the air co...

A tunning fork of frequency 340 Hz resonates in the fundamental mode with an air column of length 125 cm in a cylindrical tube closed at one end. When...

A set of 20 tuning forks is arranged in a series of increasing frequencies. If each fork gives 4 beats with respect to the preceding fork and the freq...

The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe. If the length of the closed organ pip...

Two travelling waves of equal amplitudes and equal frequencies move in opposite directions along a string. They interfere to produce a stationary wave...

A wire having a linear mass density 9.0 $$\times$$ 10$$-$$4 kg/m is stretched between two rigid supports with a tension of 900 N. The wire resonates a...

A tuning fork is vibrating at 250 Hz. The length of the shortest closed organ pipe that will resonate with the tuning fork will be __________ cm. (Tak...

Two cars X and Y are approaching each other with velocities 36 km/h and 72 km/h respectively. The frequency of a whistle sound as emitted by a passeng...

Two waves are simultaneously passing through a string and their equations are : y1 = A1 sin k(x $$-$$ vt), y2 = A2 sin k(x $$-$$ vt + x0). Given ampli...

A source and a detector move away from each other in absence of wind with a speed of 20 m/s with respect to the ground. If the detector detects a freq...

Two travelling waves produces a standing wave represented by equation,y = 1.0 mm cos(1.57 cm$$-$$1) x sin(78.5 s$$-$$1)t. The node closest to the orig...

The frequency of a car horn encountered a change from 400 Hz to 500 Hz, when the car approaches a vertical wall. If the speed of sound is 330 m/s. The...

The amplitude of wave disturbance propagating in the positive x-direction is given by $$y = {1 \over {{{(1 + x)}^2}}}$$ at time t = 0 and $$y = {1 \ov...

A closed organ pipe of length L and an open organ pipe contain gases of densities $$\rho$$1 and $$\rho$$2 respectively. The compressibility of gases a...

The mass per unit length of a uniform wire is 0.135 g/cm. A transverse wave of the form y = $$-$$ 0.21 sin (x + 30t) is produced in it, where x is in ...

The percentage increase in the speed of transverse waves produced in a stretched string if the tension is increased by 4%, will be __________%.

Two cars are approaching each other at an equal speed of 7.2 km/hr. When they see each other, both blow horns having frequency of 676 Hz. The beat fre...