Embibe Experts Solutions for Chapter: Waves, Exercise 1: Exercise 1

A copper wire is held at the two ends by rigid supports. At $30°\mathrm{C}$ the wire is just taut, with negligible tension. The speed of transverse waves in this wire at $10°\mathrm{C}$ is:

$\left(\mathrm{\alpha }=1.7\times {10}^{-5}°\mathrm{C},\mathrm{Y}=1.3\times {10}^{11} \mathrm{N}/{\mathrm{m}}^2, \mathrm{d}=9\times {10}^3 \mathrm{kg}/{\mathrm{m}}^3\right).$

Both the strings, show, in figure, are made of same material and have same cross-section. The pulleys are light. The wave speed of a transverse wave in the string $AB$ is $v_1$ and in $CD$ it is $v_2.$ The $v_1/v_2$ is

In travelling waves, the relation between particle velocity $v_p{v}_p,$ wave velocity $v$ and wave shape slope $m$ is given by

The function $y\left(x, t\right)=A{e}^{-\beta \left(x-\alpha t\right)}$ (in $\mathrm{SI}$ units) represent a travelling wave. The wave speed is

A sinusoidal wave is propagating through a medium in the direction of negative $x$-axis. The parameters of the waves are $A, \omega$ and $k.$ If the particles at $x=\frac{\lambda }{4}$ executes the motion $y\left(t\right)=$$A\sin \omega t$ then possible equation of the wave is

A source of sound is in the shape of a long narrow cylinder radiating sound waves normal to the axis of the cylinder. Two points $P$ and $Q$ are at perpendicular distances of $9 \mathrm{m}$ and $25 \mathrm{m}$  from the axis. The ratio of the amplitudes of the waves at $P$ and $Q$ is:-

Dependence of disturbances due to two waves on time is shown in the figure. The ratio of their intensities $\frac{I_1}{I_2}$ will be:-

A metal wire of linear mass density of $9.8 \mathrm{g} {\mathrm{m}}^{-1}$ is stretched with a tension of $10 \mathrm{kg}$ wt between two rigid supports $1 \mathrm{metre}$ apart. The wire passes at its middle point between the poles of a permanent magnet, and it vibrates in resonance when carrying an alternating current of frequency $n$. The frequency $n$ of the alternating source is