Waves PYQs - Last 10 Years

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).
The length of the string is : (All quantities are
in SI units.)

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. If an observer in car A detects
a frequency 2000 Hz of the sound coming from
car B, what i...

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 its fundamental frequency is :-

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 at a frequency such that the joint of
the two wires forms a node. If the number of
antinod...

A travelling harmonic wave is represented by the equation y(x,t) = 10–3sin (50t + 2x), where, x and y are in mater and t is in seconds. Which of the following is a correct statement about the wave ?

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 Hz produces first resonance when the tube is filled with water to a mark 11 cm below a refe...

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 given in the figure.

For this wave, the phase \(\phi\) 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 signal of 500 Hz to detect A and receives a reflected sound of
frequency \(\upsilon\). T...

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/s and he hears 10 beats/s. The velocity of sound is 330 m/s.
Then, u equals :

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 sound as 10–12 W/m2
]

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 occur at two successive lengths of the air column,
l1 = 30 cm and l2 = 70 cm. Then, v is e...

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. The tension in the string is :

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 vibrator of frequency 100 Hz. The separation between successive nodes on the string is close t...

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 speed of the train is reduced to 17 m/s, the frequency registered is ƒ2. If speed of sound ...

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 frequencies 480 Hz and 530 Hz.
Their respective speeds are, in ms–1,
(Given speed of sound = 300 m...

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. What will be the apparent frequency of the source when it
is moving away from the observer ...

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

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 be :

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 slightly increased and the beat frequency is found to decrease by 3Hz. If the frequency of A is ...

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 the length of the pipe ? (Speed of sound in air is \(340\,m{s^{ - 1}}\))

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 1 m. The frequency of the fork will be :

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/m3 and its Young’s modulus is 9.27 \(\times\) 1010 Pa. What will be the fundamental freque...

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 sin \(\left( {{{5\pi } \over 4}x} \right)\,\) cos(200 \(\pi\)t).
What is the speed of the ...

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 spherical bobs have uniform mass distribution. If the relative difference in the periods, ...

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 at the point O, as shown in the figure. The combination is used as a sonometer wire and k...

An observer is moving with half the speed of light towards a stationary microwave source emitting waves
at frequency 10 GHz. What is the frequency of the microwave measured by the observer? (speed of light =
3 ×108 ms–1)