Embibe Experts Solutions for Chapter: Wave Motion on a String, Exercise 4: Exercise-4

A metal wire of diameter $1 \mathrm{mm}$, is held on two knife edges separated by a distance of $50 \mathrm{cm}$. The tension in the wire is $100 \mathrm{N}$. The wire vibrating in its fundamental frequency and a vibrating tuning fork together produces $5$  beats per second. The tension in the wire is then reduced to $81 \mathrm{N}$. When the two are excited, beats are again at the same rate. Calculate:
(a) The frequency of the fork.

(b) The density of the material of wire.

The displacement of a particle executing periodic motion is given by $y=4{\cos }^2(0.5t)\sin \left(1000t\right)$. The given expression is composed by minimum:

A circular loop of rope of length $L$ rotates with uniform angular velocity $\omega$ about axis through its centre on a horizontal smooth platform. Velocity of pulse (with respect to rope) produced due to sight radial displacement is given by

A metalled wire with tension $T$ and at temperature $30º\mathrm{C}$ vibrates with its fundamental frequency of $1 \mathrm{kH}z.$ The same wire with the same tension but at $10°\mathrm{C}$ temperature vibrates with a fundamental frequency of $1.001 \mathrm{kHz}.$ The cofficient of linear expansion of the wire is

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 certain transverse sinusoidal wave of wavelength $20 \mathrm{cm}$ is moving in the positive $X$ direction. The transverse velocity of the particle at $x=0$ as a function of time is shown. The amplitude of the motion is

A wave travels on a light string. The equation of the wave is $Y=A\sin \left(kx-\omega t+30°\right).$ It is reflected from a heavy string tied to an end of the light string at $x=0.$If $64\%$of the incident energy is reflected the equation of the reflected wave is

A wire having a linear mass density of $0.05 \mathrm{gm} {\mathrm{cm}}^{-1}$ is stretched between two rigid supports with a tension of $4.5\times {10}^7$ dynes. It is observed that the wire resonates at a frequency of $420$ cycles/sec. The next higher frequency at which the same wire resonates is $490$ cycles/sec. The length of wire is approximately ?