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 $336 \mathrm{~ms}^{-1}$ )

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 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

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 speed of sound in air is $340 \mathrm{~ms}^{-1}$ and $n_1: n_2=71: 65$, then speed of observer is

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 ) of this wave is ( $x$ in metre, $t$ in second)

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 $100 \%$, then $\frac{T_2}{T_1}=$

(Linear density of the string is constant)

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 the string 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 string becomes 100 Hz , then $T_2: T_1=$

(Linear density of the string is constant)

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

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 $=336 \mathrm{~ms}^{-1}$ )

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 an observer standing at a distance of 10 m from the fixed end of the string is

(speed of sound in air $=340 \mathrm{~ms}^{-1}$ )

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 of the string is $88 \mathrm{~ms}^{-1}$. If the lift moves downwards with an acceleration of $1.9 \mathrm{~ms}^{-2}$, the speed of the transverse wave at the lower end of the string is $\left(g=10 \mathrm{~ms}^{-2}\right)$

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 (speed of sound in air $=340 \mathrm{~ms}^{-1}$ )

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, $x=$

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 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 $A B$ is equal to the frequency of the second harmonic of $C D$, then the value of $x$ is

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

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

Which of the following wave has the largest wave speed?

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 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 $\Delta f_2<\Delta f_1$, then the frequency of $B$ is

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

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 $A_1>A_2$ )

Two trucks heading in opposite directions each with speed $0.1 u$, approach each other. The speed of the sound is $u$. The driver of first truck sounds his horn of frequency 495 Hz . Let $v_1$ and $v_2$ are the frequencies heard by the driver of second truck, when the trucks approach each other and when the trucks have passed each other. The magnitude of $v_1-v_2$ is

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

A bus moving with an uniform speed of $72 \mathrm{~km} / \mathrm{h}$ towards a building blows a horn of frequency 1.7 kHz . If speed of sound in air is $340 \mathrm{~m} / \mathrm{s}$, what will be the frequency of echo heard by bus driver?