## Numerical

On a frictionless horizontal plane, a bob of mass $m=0.1 \mathrm{~kg}$ is attached to a spring with natural length $l_{0}=0.1 \mathrm{~m}$. The spring...

A stationary tuning fork is in resonance with an air column in a pipe. If the tuning fork is moved with
a speed of 2 ms−1
in front of the open end of ...

A train S1, moving with a uniform velocity of 108 km/h, approaches another train S2 standing on a platform. An observer O moves with a uniform velocit...

Two men are walking along a horizontal straight line in the same direction. The man in front walks at a speed $$1.0\,m{s^{ - 1}}$$ and the man behind ...

A stationary source emits sound of frequency $${f_0} = 492\,Hz.$$ The sound is reflected by a large car approaching the source with a speed of $$2\,m{...

Four harmonic waves of equal frequencies and equal intensities I0 have phase angles 0, $${\pi \over 3},{{2\pi } \over 3}$$ and $$\pi$$. When they are...

A stationary source is emitting sound at a fixed frequency f0, which is reflected by two cars approaching the source. The difference between the frequ...

When two progressive waves $${y_1} = 4\sin (2x - 6t)$$ and $${y_2} = 3\sin \left( {2x - 6t - {\pi \over 2}} \right)$$ are superimposed, the amplitude...

## MCQ (More than One Correct Answer)

A source, approaching with speed u towards the open end of a stationary pipe of length L, is emitting a sound of frequency fs. The farther end of the ...

In an experiment to measure the speed of sound by a resonating air column, a tuning fork of frequency $$500$$ $$Hz$$ is used. The length of the air co...

A block $$M$$ hangs vertically at the bottom end of a uniform rope of constant mass per unit length. The top end of the rope is attached to fixed rigi...

Two loudspeakers M and N are located 20m apart and emit sound at frequencies 118 Hz and 121 Hz, respectively. A car in initially at a point P, 1800 m ...

One end of a taut string of length 3 m along the x-axis is fixed at x = 0. The speed of the waves in the string is 100 ms$$-$$1. The other end of the ...

Two vehicles, each moving with speed u on the same horizontal straight road, are approaching each other. Wind blows along the road with velocity w. On...

A horizontal stretched string, fixed at two ends, is vibrating in its fifth harmonic according to the equation
y(x, t) = (0.01 m) sin[(62.8 m$$-$$1)x]...

## MCQ (Single Correct Answer)

A musical instrument is made using four different metal strings, 1, 2, 3 and 4 with mass per unit length $$\mu $$, 2$$\mu $$, 3$$\mu $$ and 4$$\mu $$ ...

A musical instrument is made using four different metal strings, 1, 2, 3 and 4 with mass per unit length $$\mu $$, 2$$\mu $$, 3$$\mu $$ and 4$$\mu $$ ...

A student is performing the experiment of resonance Column. The diameter of the column tube is
4 cm. The frequency of the tuning fork is 512 Hz. The a...

A police car with a siren of frequency 8 kHz is moving with uniform velocity 36 km/hr towards a tall
building which reflects the sound waves. The spee...

Column I shows four systems, each of the same length L, for producing standing waves. The lowest possible natural frequency of a system is called its ...

A hollow pipe of length 0.8 m is closed at one end. At its open end a 0.5 m long uniform string is vibrating
in its second harmonic and it resonates w...