B M Sharma Solutions for Chapter: Sound Waves and Doppler Effect, Exercise 3: Exercises

In the figure shown an observer $O_1$ floats (static) on water surface with ears in air while another observer $O_2$ is moving upwards with constant velocity $V_1=\frac{V}{5}$ in water. The source moves down with constant velocity $V_s=\frac{V}{5}$ and emits sound of frequency $f^{\text{'}}.$ The velocity of sound in air is $V$ and that in water is $4 \mathrm{V}$. For the situation shown in figure.

Two tuning forks $A$ and $B$are vibrating at the same frequency $256 \mathrm{Hz}$. A listener is standing midway between the forks. If both tuning forks move to the right with a velocity of $5 \mathrm{m}/\mathrm{s}$, find the number of beats heard per second by the Tistener (speed of sound in air is $330 \mathrm{m}/\mathrm{s}$ ).

A driver in a stationary car horns which produces monochromatic sound waves of frequency $n=1000 \mathrm{Hz}$, normally towards a reflecting wall. If the wall approaches the car with a velocity $u=3.3 \mathrm{m}/\mathrm{s}$, calculate the frequency of sound reflected from wall and heard by the driver. What is the percentage change of sound frequency on reflection from the wall?

A source of sound of frequency $256 \mathrm{Hz}$ is moving towards a wall with a velocity of $5 \mathrm{m}/\mathrm{s}$. How many beats per second will be heard by an observer $O$ standing in such a position that the source $S$ is between $O$ and wall? $(c=330 \mathrm{m}/\mathrm{s})$

A vibrating tuning fork tied to the end of a string $1.988 \mathrm{m}$ long is whirled round a circle. If it makes two revolutions in a second, calculate the ratio of the frequencies of the highest and the lowest notes heard by an observer situated in the plane of the tuning fork. Velocity of sound is $350 \mathrm{m}/\mathrm{s}$.

A source of sonic oscillations with frequency $n=1700 \mathrm{Hz}$ and a receiver are located on the same normal to a wall. Both the source and receiver are stationary, and the wall recedes from the source with velocity $u=6.0 \mathrm{cm}/\mathrm{s}$. Find the beat frequency (in $\mathrm{Hz}$ ) registered by the receiver. The velocity of sound is $v=340 \mathrm{m}/\mathrm{s}$.

A locomotive approaching a crossing at a speed of $80\mathrm{mi}/\mathrm{h}$ sounds a whistle of frequency $400 \mathrm{Hz}$ when $1\mathrm{mi}$ from the crossing. There is no wind, and the speed of sound in air is$0.200\mathrm{mi}/\mathrm{s}$. What frequency is heard by an observer $0.60\mathrm{mi}$ from the crossing on the straight road which crosses the railroad at right angles?

A whistle of frequency $f_0=1300 \mathrm{Hz}$ is dropped from a height $H=505 \mathrm{m}$ above the ground. At the same time, a detector is projected upwards with velocity $v=50{ \mathrm{ms}}^{-1}$ along the same line. If the velocity of sound is $v=300{ \mathrm{ms}}^{-1}$, find the frequency (in $\mathrm{Hz}$ ) detected by the detector after $t=5 \mathrm{s}.$