Doppler effect

An audio transmitter (T) and a receiver (R) are hung vertically from two identical massless strings of length 8 m with their pivots well separated along the $X$ axis. They are pulled from the equilibrium position in opposite directions along the $X$ axis by a small angular amplitude $\theta_0 = \cos^{-1}(0.9)$ and released simultaneously. If the natural frequency of the transmitter is 660 Hz and the speed of sound in air is 330 m/s, the maximum variation in the frequency (in Hz) as measured by the receiver (Take the acceleration due to gravity $g = 10\ \mathrm{m/s^2}$) is _____.

A source (S) of sound has frequency $240\,\mathrm{Hz}$. When the observer (O) and the source move towards each other at a speed $v$ with respect to the ground (as shown in Case 1 in the figure), the observer measures the frequency of the sound to be $288\,\mathrm{Hz}$. However, when the observer and the source move away from each other at the same speed $v$ with respect to the ground (as shown in Case 2 in the figure), the observer measures the frequency of sound to be $n\,\mathrm{Hz}$. The value of $n$ is _____.

When only $S_2$ is emitting sound and it is at $Q$, the frequency of sound measured by the detector in Hz is _____.

Consider both sources emitting sound. When $S_2$ is at $R$ and $S_1$ approaches the detector with a speed $4\ \mathrm{m\,s^{-1}}$, the beat frequency measured by the detector is _____ Hz.

An observer moves towards a stationary source of sound with a velocity equal to one-fifth of the velocity of sound. The percentage change in the frequency will be :

An employee of a factory moving away from his workplace by a car listens to the siren of the factory. He drives the car at the speed of 72 kmh$^{-1}$ in the direction of wind which is blowing at 72 kmh$^{-1}$ speed. Frequency of siren is 720 Hz. The employee hears an apparent frequency of ______ Hz.

(Assume speed of sound to be 340 ms$^{-1}$)

An observer is riding on a bicycle and moving towards a hill at 18 kmh$^{-1}$. He hears a sound from a source at some distance behind him directly as well as after its reflection from the hill. If the original frequency of the sound as emitted by source is 640 Hz and velocity of the sound in air is 320 m/s, the beat frequency between the two sounds heard by observer will be ______ Hz.

When a car is approaching the observer, the frequency of horn is 100 Hz. After passing the observer, it is 50 Hz. If the observer moves with the car, the frequency will be $\dfrac x3$ Hz where $x=$ ______.

The frequency of echo will be ______ Hz if the train blowing a whistle of frequency 320 Hz is moving with a velocity of 36 km/h towards a hill from which an echo is heard by the train driver. Velocity of sound in air is 330 m/s.

A source, approaching with speed $u$ towards the open end of a stationary pipe of length $L$, is emitting a sound of frequency $f_s$. The farther end of the pipe is closed. The speed of sound in air is $v$ and $f_0$ is the fundamental frequency of the pipe. For which of the following combination(s) of $u$ and $f_s$, will the sound reaching the pipe lead to a resonance?

A stationary tuning fork is in resonance with an air column in a pipe. If the tuning fork is moved with a speed of $2\ \mathrm{m\,s^{-1}}$ in front of the open end of the pipe and parallel to it, the length of the pipe should be changed for the resonance to occur with the moving tuning fork. If the speed of sound in air is $320\ \mathrm{m\,s^{-1}}$, the smallest value of the percentage change required in the length of the pipe is ______.

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 velocity of 36 km/h towards S2, as shown in figure. Both the trains are blowing whistles of same frequency 120 Hz. When O is 600 m away from S2 and distance between S1 and S2 is 800 m, the number of beats heard by O is ______.

[Speed of the sound = 330 m/s]

Two men are walking along a horizontal straight line in the same direction. The man in front walks at a speed $1.0\ \mathrm{m\,s^{-1}}$ and the man behind walks at a speed $2.0\ \mathrm{m\,s^{-1}}$. A third man is standing at a height 12 m above the same horizontal line such that all three men are in a vertical plane. The two walking men are blowing identical whistles which emit a sound of frequency 1430 Hz. The speed of sound in air is $330\ \mathrm{m\,s^{-1}}$. At the instant, when the moving men are 10 m apart, the stationary man is equidistant from them. The frequency of beats in Hz, heard by the stationary man at this instant, is ______.

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 $2\ \mathrm{ms^{-1}}$. The reflected signal is received by the source and superposed with the original. What will be the beat frequency of the resulting signal in Hz? (Given that the speed of sound in air is $330\ \mathrm{ms^{-1}}$ and the car reflects the sound at the frequency it has received).

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 = $3\times10^8$ ms$^{-1}$)

Two loudspeakers $M$ and $N$ are located 20 m apart and emit sound at frequencies 118 Hz and 121 Hz, respectively. A car is initially at a point $P$, 1800 m away from the midpoint $Q$ of the line $MN$ and moves towards $Q$ constantly at 60 km/hr along the perpendicular bisector of $MN$. It crosses $Q$ and eventually reaches a point $R$, 1800 m away from $Q$. Let $\nu(t)$ represent the beat frequency measured by a person sitting in the car at time $t$. Let $\nu_P$, $\nu_Q$ and $\nu_R$ be the beat frequencies measured at locations $P$, $Q$ and $R$, respectively. The speed of sound in air is $330\ \mathrm{m\,s^{-1}}$. Which of the following statement(s) is(are) true regarding the sound heard by the person?

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 sound is 330 m/sec :

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 horn of the toy car is close to :

A train is moving on a straight track with speed 20 ms$^{-1}$. 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 (speed of sound = 320 ms$^{-1}$) close to :

A bat moving at 10 ms$^{-1}$ towards a wall sends a sound signal of 8000 Hz towards it. On reflection it hears a sound of frequency $f$. The value of $f$ in Hz is close to (speed of sound = 320 ms$^{-1}$)