Doppler Effect

A radar operates at wavelength $50.0 \mathrm{cm}$. If the beat frequency between the transmitted signal and the signal reflected from aircraft $\left(∆\nu \right)$ is $1 \mathrm{kHz}$, then velocity(in $\mathrm{km} {\mathrm{h}}^{-1}$) of the aircraft will be

A police car moving at $30 \mathrm{m} {\mathrm{s}}^{-1}$, chases a motorcyclist. The policeman sounds his horn at $180 \mathrm{Hz}$, while both of them move towards a stationary siren of frequency $160 \mathrm{Hz}$. The speed (in $\mathrm{m} {\mathrm{s}}^{-1}$) of the motorcyclist to the nearest integer, if it is given that he does not observe any beats is $\alpha$. Write the value of $\left[\alpha \right],$ where $\alpha$ is the greatest integer function.

(Take, the speed of sound $=330 \mathrm{m} {\mathrm{s}}^{-1}$ ).

An observer rides with a sound source of frequency $f$ and moving with velocity $v$ towards a large vertical wall. Considering the velocity of sound waves as $c,$ find;

(a) The number of waves striking the wall per second.

(b) The wavelength of the reflected wave.

(c) The frequency of the reflected wave as observed by the observer.

(d) Beat frequency heard by the observer.

An observer moves towards a stationary source of sound with a velocity one-fifth of the velocity of sound. The percentage change in the apparent frequency is

A bus is moving with a velocity of $5 \mathrm{m} {\mathrm{s}}^{-1}$ towards a huge wall. The driver sounds a horn of frequency $165 \mathrm{Hz}$. If the speed of sound in air is $335 \mathrm{m} {\mathrm{s}}^{-1}$, Calculate the number of beats heard per second by a passenger on the bus. Take speed of sound $=335 \mathrm{m} {\mathrm{s}}^{-1}$.

Two tuning forks $A$ and $B$ lying on opposite sides of observer $O$ and of natural frequency $85 \mathrm{Hz}$ move with velocity $10 \mathrm{m}/\mathrm{s}$ relative to a stationary observer $O$. Fork $A$ moves away from the observer while the fork $B$ moves towards him. Wind with a speed $10 \mathrm{m}/\mathrm{s}$ is blowing in the direction of motion of fork $A$. Find the beat frequency measured by the observer in $\mathrm{Hz}$. (Take speed of sound in air as $340 \mathrm{m}/\mathrm{s}$)

A whistle of frequency 540 Hz rotates in a horizontal circle of radius 2 m at an angular speed of 15 $\mathrm{r}\mathrm{a}\mathrm{d}{\mathrm{s}}^{-1}$. The highest frequency heard by a listener at rest at large distance with respect to the centre of circle (velocity of sound in air =$330 \mathrm{m} {\mathrm{s}}^{-1}$)

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 sound is 330 m/sec:

A car is moving with $90\mathrm{ }\mathrm{km} {\mathrm{h}}^{-1}$ blows a horn of $150\mathrm{ }\mathrm{Hz}$, towards a cliff. The frequency of the reflected sound heard by the driver will be (speed of sound in air is $340\mathrm{ }\mathrm{m} {\mathrm{s}}^{-1}$ )

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

Two sources of sound $S_1$ and $S_2$ produce sound waves of same frequency $660 \mathrm{H}\mathrm{z}.$ A listener is moving from source $S_1$ towards $S_2$ with a constant speed $u_0\mathrm{ }\mathrm{m} {\mathrm{s}}^{-1}$ and he hears $10 \mathrm{b}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{s} {\mathrm{s}}^{-1}.$ The velocity of sound is $330 \mathrm{m} {\mathrm{s}}^{-1}.$ Then, $u_0$ equals:

A source of sound $S$ is moving with a velocity of $50\mathrm{ }\mathrm{m} {\mathrm{s}}^{-1}$ towards a stationary observer. The observer measures the frequency of the source as $1000\mathrm{ }\mathrm{H}\mathrm{z}.$ What will be the apparent frequency of the source when it is moving away from the observer after crossing him? (Take velocity of sound in air is $350\mathrm{ }\mathrm{m} {\mathrm{s}}^{-1}$ )

A siren emitting a sound of frequency $\mathrm{800\; Hz}$ moves away from an observer towards a cliff at a speed of $15\mathrm{ }\mathrm{m }{\mathrm{s}}^{-1}$. Then, the frequency of sound that the observer hears in the echo reflected from the cliff is
(Take velocity of sound in air $=330\mathrm{ }\mathrm{m }{\mathrm{s}}^{-1}$)

An observer is moving with half the speed of light towards a stationary microwave source emitting waves at frequency $10 \mathrm{GHz}$. What is the frequency of the microwave measured by the observer? (speed of light $=3\times {10}^8\mathrm{ m} {\mathrm{s}}^{-1}$)

A source of sonic oscillations with frequency $f_0=1000 \mathrm{Hz}$ moves at right angle to the wall with a velocity $u=0.17 \mathrm{m} {\mathrm{s}}^{-1}$. Two stationary receivers ${\text{R}}_1$ and ${\text{R}}_2$ are located on a straight line, coinciding with the trajectory of the source, in the following succession: ${\text{R}}_1\text{-}$ source ${\text{-R}}_2\text{-}$ wall. The velocity of sound is equal to $340$ $\mathrm{m} {\mathrm{s}}^{-1}$. If the beat frequency heard by $R_1$ is $n_1 \mathrm{Hz}$ and by $R_2$ is $n_2 \mathrm{Hz}$, find $\left(n_1+n_2\right)$.

A source on a swing which is covering an angle $\theta$ from the vertical is producing a frequency $v.$ The source is distant $d$ from the place of support of the swing. If velocity of sound is $c$, acceleration due to gravity is $g$, then the maximum and minimum frequency heard by a listener in front of swing is

Policemen buzz a whistle frequency $400 \mathrm{Hz}$. A car driver is approaching the policemen. The speed of a car is $72 \mathrm{km} {\mathrm{h}}^{-1}.$ Find out the change in frequency experienced by the driver when a driver approaches the policemen, and after he crosses the policemen? [Velocity of sound is$\left.350{ \mathrm{m} \mathrm{s}}^{-1}\right]$.

Assertion: Motion of source with respect to the stationary observer is not equivalent to the motion of an observer with respect to a stationary source.

Reason: Doppler formula for a sound waves is symmetric with respect to the speed of the source and speed of the observer.

Two sources are at a finite distance apart. They emit sounds of wavelength $\lambda$. An observer situated between them on the line joining approaches one source with speed $u$. Then the number of beats heard by observer will be :

When an engine passes near to a stationary observer then its apparent frequencies occurs in the ratio $\frac{5}{3}$. If the velocity of sound is $340 \mathrm{m} {\mathrm{s}}^{-1}$ then the speed of the engine is