Waves

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)

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. Calculate the
frequency heard by driver of second engine before they pass each other. Speed of sou...

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 hear 5 beats per second. If the velocity of sound in air is 340 m/s, the frequency of the hor...

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 fundamental frequency of the air column is now :

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 string. The time taken to reach the supports is :
(take \({\,\,g = 10m{s^{ - 2}}}\) )

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 change in the frequency heard by a person standing near the track as the train passes him is...

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 lie below \(1250\) \(Hz\). The velocity of sound in air is \(340\) \(m/s\).

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 frequency of steel if density and elasticity of steel are \(7.7 \times {10^3}\,kg/{m^3}\) and $$2....

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 water. The fundamental frequency of the air-column is now :

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

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( {{t \over {0.04\left( s \right)}} - {x \over {0.50\left( m \right)}}} \right)} \right].$...

Three sound waves of equal amplitudes have frequencies \(\left( {v - 1} \right),\,v,\,\left( {v + 1} \right).\) They superpose to give beats. The number of beats produced per second will be :

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 electric siren. How far has the motor cycle gone when the driver hears the frequency of the...

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 wavelength and the time period of the wave are \(0.08\) \(m\) and \(2.0s\), respectively, then $$...

While measuring the speed of sound by performing a resonance column experiment, a student gets the first resonance condition at a column length of \(18\) \(cm\) during winter. Repeating the same experiment during summer, she measures the co...

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 velocity of sound in air is \(300\,m{s^{ - 1}}.\) If the person can hear frequencies upto a ma...

A string is stretched between fixed points separated by \(75.0\) \(cm.\) It is observed to have resonant frequencies of \(420\) \(Hz\) and \(315\) \(Hz\). There are no other resonant frequencies between these two. Then, the lowest resonant ...

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 prong of the fork \(2.\) When the tuning forks are sounded again, \(6\) beats per second are ...

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 apparent frequency ?

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

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 \(2\) beats per second when the tension in the piano string is slightly increased. The freque...

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

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 apart. The wire passes at its middle point between the poles of a permanent magnet, and it vib...

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 it then produces \(2\) beats/sec. The frequency of the unknown fork is