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

Three sinusoidal waves with the same angular frequency but with different amplitudes $A, \frac{A}{2}, \frac{A}{3}$ and phase angles $0, \frac{\pi }{2}$ and $\pi$ respectively move along the same direction and superpose with each other. The amplitude of the resultant wave is given by

The equation of a progressive wave is, $y=0.02\sin 2\pi \left[\frac{t}{0.01}-\frac{x}{0.3}\right]$ where, $x$ and $y$ are in $\mathrm{meters}$ and $t$ is in $\mathrm{second}$. The velocity of propagation of the wave is,

A travelling wave on a string is given by $y=A\sin \left[\alpha x+\beta t+\frac{\mathrm{\pi }}{6}\right]$. The displacement and velocity of oscillation of a point $\alpha =0.56 {\mathrm{cm}}^{-1}$, $\beta =12 {\sec }^{-1}$, $A=7.5 \mathrm{cm}$, $x=1 \mathrm{cm}$ and $t=1 \mathrm{s}$ is

If the ratio of amplitudes of two waves at any point in the medium is $1:3$, then the ratio of maximum and minimum intensities due to their superposition will be

The equation of a progressive wave is given by, $y=a\sin (\omega t-kx)$. Then, which of the following equations is not correct?

The phase difference between two points separated by $0.8 \mathrm{m}$ in a wave of frequency $100 \mathrm{Hz}$ is $\frac{\pi }{2}.$ What is the wave velocity (in $\mathrm{m} {\mathrm{s}}^{-1}$)?

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: