Waves PYQs - Last 5 Years

A metal rod of length 125 cm is clamped at its midpoint. If the speed of the sound in the metal is $5000 \mathrm{~ms}^{-1}$, then the fundamental frequency of the longitudinal vibrations of the rod is

An air column in a tube of length 50 cm , closed at one end is vibrating in its fifth harmonic. The phase difference between a particle at the open end and a particle at 42 cm from the open end is

A car moving towards a cliff emits sound of frequency ' $n$ '. If the difference in frequencies of the horn and its echo heard by the driver of the car is $10 \%$ of ' $n$ ', then the speed of the car is nearly
(Speed of sound in air is $33...

The air columns in two tubes closed at one end vibrating in their fundamental modes produce 2 beats per second. The number of beats produced per second when the same tubes are vibrated in their fundamental mode with their both ends open are...

A string vibrates in its fundamental mode when a tension $T_1$ is applied to it. If the length of the string is decreased by $25 \%$ and the tension applied is changed to $T_2$, the fundamental frequency of the string increases by $100 \%$,...

A sound wave of frequency 210 Hz travels with a speed of $330 \mathrm{~ms}^{-1}$ along the positive $X$-axis. Each particle of the wave moves a distance of 10 cm between the two extreme points. The equation of the displacement function ( s ...

Two tuning forks of frequencies 320 Hz and 323 Hz are vibrated together. The time interval between a maximum sound and its adjacent minimum sound heard by an observer is

The frequency of sound heard by an observer moving towards a stationary source with certain speed is $n_1$ and if the observer moves away from the same source with same speed, the frequency of sound heard by the observer is $n_2$. If the sp...

Two sound waves each of intensity $I$ are superimposed. If the phase difference between the waves is $\frac{\pi}{2}$, then the intensity of the resultant wave is

The fundamental frequency of transverse wave of a stretched string subjected to a tension $T_1$ is 300 Hz . If the length of the string is doubled and subjected to a tension of $T_2$, the fundamental frequency of the transverse wave in the ...

If the lengths of the open and closed pipes are in the ratio of $2: 3$, then the ratio of the frequencies of the third harmonic of the open pipe and the fifth harmonic of the closed pipe is

The equation of a transverse wave propagating on a stretched string is given by $y=3 \sin (4 x+200 t)$, where $x$ and $y$ are in metre and the time ' $t$ ' is in second. If the tension applied to the string is 500 N , the linear density of ...

A car travelling at a speed of 54 kmph towards a wall sounds horn of frequency 400 Hz . The difference in the frequencies of two sounds, one received directly from the car and other reflected from the wall noticed by a person standing betwe...

The speed of a transverse wave in a stretched string $A$ is $v$. Another string $B$ of same length and same radius is subjected to same tension. If the density of the material of the string $B$ is $2 \%$ more than that of $A$ then the speed...

A boy standing on a platform observes the frequency of a train horn as it passes by. The change in the frequency noticed as the train approaches and recedes him with a velocity of 108 kmph is (speed of sound in air $=330 \mathrm{~ms}^{-1}$ ...

If three sources of sound of frequencies $(n-1), n$ and $(n+1)$ are vibrated together, the number of beats produced and heard per second respectively are

Two closed pipes when sounded simultaneously in their fundamental modes produce 6 beats per second. If the length of the shorter pipe is 150 cm , then the length of the longer pipe is(Speed of sound in air $=336 \mathrm{~ms}^{-1}$ )

The tension applied to a metal wire of one metre length produces an elastic strain of $1 \%$. The density of the metal is $8000 \mathrm{kgm}^{-3}$ and Young's modulus of the metal is $2 \times 10^{11} \mathrm{Nm}^{-2}$. The fundamental freq...

The displacement equations of sound waves produced by two sources are given by $y_1=5 \sin 400 \pi t$ and $y_2=8 \sin 408 \pi t$, where $t$ is time in seconds. If the waves are produced simultaneously, the number of beats produced per minut...

The difference between the fundamental frequencies of an open pipe and a closed pipe of same length is 100 Hz . The difference between the frequencies of the second harmonic of the open pipe and the third harmonic of the closed pipe is

A source at rest emits sound waves of frequency 102 Hz . Two observers are moving away from the source of sound in opposite directions each with a speed of $10 \%$ of the speed of sound. The ratio of the frequencies of sound heard by the ob...

The path difference between two particles of a sound wave is 50 cm and the phase difference between them is $1.8 \pi$. If the speed of sound in air is $340 \mathrm{~ms}^{-1}$, the frequency of the sound wave is

Among the following statements, the correct statement for a wave is

A source and an observer move away from each other with same velocity of $10 \mathrm{~ms}^{-1}$ with respect to ground. If the observer finds the frequency of sound coming from the source as 1980 Hz , then actual frequency of the source is ...

One end of a string is tied to the ceiling of a lift and a load is attached at the bottom end of the string. When the lift is moving upwards with an acceleration of 2.1 $\mathrm{ms}^{-2}$, the speed of the transverse wave at the lower end o...

A source emitting sound is tied to one end of a string of length 50 cm and is rotated with an angular speed of $40 \mathrm{rad} \mathrm{s}^{-1}$ in the horizontal plane. The ratio of the maximum and minimum frequencies of the sound heard by...

If the seventh harmonic of a closed pipe is in unison with fourth harmonic of an open organ pipe, then the ratio of length of closed pipe to that of open pipe is

An observer moves towards a stationary source of sound, with a speed of one fifth of the speed of sound. The apparent increase in the frequency heard by the observer is

A wave is given by $y=5 \times 10^{-3} \sin \left(12.5 \pi x-\frac{\pi}{2} t\right)$. Then its wavelength and time period are respectively ( $y$ and $x$ are in metres and $t$ is in seconds)

A tuning fork $A$ of frequency 250 Hz and another tuning fork $B$ of frequency $x$ produced 5 beats per second when vibrated together. If the fork $B$ is waxed and vibrated together with $A$, then 3 beats per second are produced. Then, $x=$...

A heavy uniform rope is suspended vertically from a ceiling and is in equilibrium. A pulse is generated at the bottom end of the rope as shown. As the pulse travels up the rope, its acceleration at any instant is
( $g$ is acceleration due t...

A wave is given by the equation $y=(0.02) \sin (\pi x-8 \pi /$ then the velocity of the wave is $(y$ and $x$ are in metre and $t$ is in second)

A rod of length $L$ and negligible mass is suspended by two identical strings $A B$ and $C D$ as shown in the figure A mass $M$ is suspended from point $O$ which is at a distance $x$ from $B$. If the frequency of the first harmonic of $A B$...

An observer moves towards a stationary source of sound with a speed $\frac{1}{5}$ th that of sound. The frequency of ${ }^{\text {th }}$ sound emitted by the source of $f$. The apparent frequency recorded by the observer is

Which of the following wave has the largest wave speed?

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 new fundamental frequency is

Two strings $A$ and $B$ produce beat of frequency $\Delta f_1>0$. The tension in string $A$ is slightly increased and the beat frequency is found to be $\Delta f_2>0$. If the original frequency of $A$ is $f_0$ and $\Delta f_2<\Delta f_1$, t...

A wire of length 0.4 m stretched at both ends vibrates 250 times per second. If the length of the wire is increased by 0.1 m and the stretching force is reduced to $1 / 4$ th of its original value, then the new frequency is

Two waves of amplitudes $A_1$ and $A_2$ respectively, are superimposed. The ratio between the maximum and minimum intensities of the resultant waves is $9: 4$.
The value of $\frac{A_2}{A_1}$ is (assume $A_1>A_2$ )

The distance between two successive minima of a transverse wave is 2.7 m . Five crests of the wave pass a given point along the direction of travel every 15.0 s . The speed of the wave is