D. C. Pandey Solutions for Chapter: Sound Waves, Exercise 8: Exercises

A tuning fork whose natural frequency is $440 \mathrm{Hz}$, is placed just above the open end of a tube that contains water. The water is slowly drained from the tube while the tuning fork remains in place and is kept vibrating. The sound is found to be enhanced when the air column is $60 \mathrm{cm}$ long and when it is $100 \mathrm{cm}$ long. Find the speed of sound in air.

A piano wire $A$ vibrates at a fundamental frequency of $600 \mathrm{Hz}$. A second identical wire $\mathit{B}$ produces $6$ beats per second with it when the tension in $A$ is slightly increased. Find the ratio of the tension in $A$ to the tension in $B$.

A tuning fork of frequency $256 \mathrm{Hz}$ produces $4$ beats per second with a wire of length $25 \mathrm{cm}$ vibrating in its fundamental mode. The beat frequency decreases when the length is slightly shortened. What could be the minimum length by which the wire be shortened so that it produces no beats with the tuning fork?

Show that when the speed of the source and the observer are small compared to the speed of sound in the medium, the change in frequency becomes independent of the fact whether the source is moving or the observer.

A sound source moves with a speed of $80 \mathrm{m} {\mathrm{s}}^{-1}$ relative to a still air toward a stationary listener. The frequency of sound is $200 \mathrm{Hz}$ and speed of sound in air is $340 \mathrm{m} {\mathrm{s}}^{-1}$.
(a) Find the wavelength of the sound between the source and the listener.
(b) Find the frequency heard by the listener.

A rail-road train is traveling at $30 \mathrm{m} {\mathrm{s}}^{-1}$ in still air. The frequency of the note emitted by the locomotive whistle is $500 \mathrm{Hz}$.

What is the wavelength of the sound waves,
(a) in front of the locomotive?
(b) behind the locomotive?

What is the frequency of the sound heard by a stationary listener,
(c) in front of the locomotive?
(d) behind the locomotive? Speed of sound in air is $344 \mathrm{m} {\mathrm{s}}^{-1}$.

For a certain organ pipe, three successive resonance frequencies are observed at $425, 595$ and $765 \mathrm{Hz}$, respectively. Taking the speed of sound in air to be $340 \mathrm{m} {\mathrm{s}}^{-1}$ ,
(a) explain whether the pipe is closed at one end or open at both ends.
(b) determine the fundamental frequency and length of the pipe.

Two tuning forks $A$ and $B$ sounded together give $8$ beats per second. With an air resonance tube closed at one end, the two forks give resonances when the two air columns are $32 \mathrm{cm}$ and $33 \mathrm{cm}$, respectively. Calculate the frequencies of forks.