Embibe Experts Solutions for Chapter: Mechanical Wave, Exercise 1: Exercise 1

A transverse sinusoidal wave moves along a string in the positive $x$-direction at a speed of $10 \mathrm{cm} {\mathrm{s}}^{-1}$. The wavelength of the wave is $0.5 \mathrm{m}$ and its amplitude is $10 \mathrm{cm}$. At a particular time $t$, the snap-shot of the wave is shown in the figure The velocity of the point $P$ when its displacement is $5 \mathrm{cm}$ is.

Assertion : A wave can be represented by function $y=f(kx\pm \omega t).$ 

Reason : Because it satisfies the differential equation
$\frac{{\partial }^2\mathrm{y}}{\partial {\mathrm{x}}^2}=\frac{1}{{\mathrm{v}}^2}\left(\frac{{\partial }^2\mathrm{y}}{\partial {\mathrm{t}}^2}\right)\text{ where }\mathrm{v}=\frac{\omega }{\mathrm{k}}$

A steel wire of length $1 \mathrm{m}$ and mass $0.1 \mathrm{kg}$ and having a uniform cross-sectional area of ${10}^{-6} {\mathrm{m}}^2$ is rigidly fixed at both ends. The temperature of the wire is lowered by $20º\mathrm{C}$ if the transverse waves are set up plucking the string in the middle the frequency of the fundamental note of vibration is

$\left({\mathrm{Y}}_{\text{steel }}=2\times {10}^{11}\mathrm{N}/{\mathrm{m}}^2 {\mathrm{\alpha }}_{\mathrm{steel}}=1.21\times {10}^{-5}/º\mathrm{C}\right)$

A warship is fitted with SONAR operating at a frequency of $42 \mathrm{kHz}$. A submarine is approaching the ship with a speed of $72 \mathrm{km} {\mathrm{hr}}^{-1}$. If the speed of sound is $1400 \mathrm{m} {\mathrm{s}}^{-1}$, what will be the frequency of the sound received after being reflected from the submarine?

A transverse sine wave moves along a string in the positive $x$-direction at a speed of $20 \mathrm{cm} {\mathrm{s}}^{-1}.$ The wavelength of the wave is $1 \mathrm{m}$ and its amplitude is $10 \mathrm{cm}.$ The snapshot of the wave is shown in the figure. The acceleration and velocity of point $P$ whose displacement at this instant is $5 \mathrm{cm}$ are ${\overrightarrow{a}}_p$ and ${\overrightarrow{v}}_p$ respectively. Then

A sound absorber attenuates the sound level by $20 \mathrm{dB}$. The intensity decreases by a factor of

If two closed organ pipes of $750 \mathrm{cm}, 770 \mathrm{cm}$ length are sounded together in the fundamental mode, then $3$ beats per second are produced. Based on this observation, find the velocity of sound in $\mathrm{m} {\mathrm{s}}^{-1}$:

The two consecutive harmonics of a tube closed at one end and open at the other end are $220 \mathrm{Hz}$ and $260 \mathrm{Hz}$. The fundamental frequency of the system is $n \mathrm{Hz}$. The value of $n$ is: