Embibe Experts Solutions for Chapter: Wave Motion on a String, Exercise 7: Exercise (Analytical Questions)

Transverse wave of same frequency are generated in two steel wires $A \text{and} B$. The diameter of $A$ is twice of $B$ and the tension in $A$ is half of that in $B$. The ratio of velocities of waves in $A \text{and} B$ is,

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 snapshot of the wave is shown in figure. The velocity of $P$ when its displacement is $5 \mathrm{cm}$ is,

A sound source of frequency $170 \mathrm{Hz}$ is placed near a wall. A man walking from the source towards the wall finds that there is a periodic rise and fall of sound intensity. If the speed of sound in air is $340 {\mathrm{ms}}^{-1}$, the distance (in metre) separating the two adjacent positions of minimum intensity is:

A vibrator makes 150 cm of a string to vibrate in 6 loops in the longitudinal arrangement when it is stretched by 150 N. The entire length of the string is  then weighed and is found to weigh 400 mg. Then

The equation of a plane progressive wave is $y=0.02\sin 8\pi \left[t-\frac{x}{20}\right].$ When it is reflected at a rarer medium (medium with higher velocity) at $x=0,$ its amplitude becomes $75\%$ of its previous value. The equation of the reflected wave is

A sonometer wire resonates with a given tuning fork forming standing waves with five antinodes between the two bridges when a mass of $9 \mathrm{kg}$ is suspended from the wire. When this mass is replaced by mass $M$, the wire resonates with the same tuning fork forming three antinodes for the same positions of the bridges. Then, find the value of square root of $M$.

A wave $y=10\sin (ax+bt)$ is reflected from a dense medium at origin. If $81\%$ of energy is reflected, then the equation of reflected wave is,

A tuning fork gives $4$ beats with $50 \mathrm{cm}$ length of a sonometer wire. If the length of the wire is shortened by $1 \mathrm{cm},$ the number of beats is still the same.The frequency(in Hz) of the fork is :-