B M Sharma Solutions for Chapter: Superposition and Standing Waves, Exercise 3: Exercises

If a string fixed at both ends having fundamental frequency of $240 \mathrm{Hz}$ is vibrated with the help of a tuning fork having frequency $280 \mathrm{Hz},$ then the

A string of length $0.4 \mathrm{~m}$ and mass $10^{-2} \mathrm{~kg}$ is clamped at one end. The tension in the string is $1.6 \mathrm{~N}$. The identical wave pulses are generated at the free end after regular interval of time, $\Delta t$. The minimum value of $\Delta t$, so that a constructive interference takes place between successive pulses is

A train of sound waves is propagated along an organ pipe and gets reflected from an open end. If the displacement amplitude of the waves (incident and reflected) are $0.002 \mathrm{cm},$ the frequency is $1000 \mathrm{Hz}$ and wavelength is $40 \mathrm{cm}.$ Then, the displacement amplitude of vibration at a point at distance $10 \mathrm{cm}$ from the open end, inside the pipe, is

A source of sound attached to the bob of a simple pendulum execute $SHM\mathit{.}$ The difference between the apparent frequency of sound as received by an observer during its approach and recession at the mean position of the $SHM$ motion is $2\%$ of the natural frequency of the source. The velocity of the source at the mean position is (velocity of sound in the air is $340 \mathrm{m} {\mathrm{s}}^{-1}$ )

[Assume velocity of sound source $<<$ velocity of sound in air]

Two canoes are $10 \mathrm{m}$ apart on a lake. Each bobs up and down with a period of $4.0 \mathrm{s}.$ When one canoe is at its highest point, the other canoe is at its lowest point. Both canoes are always within a single cycle of the waves. The speed of wave is.

A resonance occurs with a tuning fork and an air column of size $12 \mathrm{cm}.$ The next higher resonance occurs with an air column of $38 \mathrm{cm}.$ What is the frequency of the tuning fork? Assume that the speed of sound is $312 \mathrm{m} {\mathrm{s}}^{-1}.$

In a resonance tube experiment, the first two resonances are observed at length $10.5 \mathrm{cm}$ and $29.5 \mathrm{cm}.$ The third resonance is observed at the length $\dots \dots \dots ..\mathrm{cm}$

The two pipes are submerged in sea water, arranged as shown in figure. Pipe $A$ with length $L_{\mathrm{A}}=1.5 \mathrm{m}$ and one open end, contains a small sound source that sets up the standing wave with the second lowest resonant frequency of that pipe. Sound from pipe $A$ sets up resonance in pipe $B$, which has both ends open. The resonance is at the second lowest resonant frequency of pipe $B$. The length of the pipe $B$ is