Embibe Experts Solutions for Chapter: Mechanical Wave, Exercise 1: JEE Main - 11th April 2015

The frequency of echo will be _____ $\mathrm{Hz}$ if the train blowing a whistle of frequency $320 \mathrm{Hz}$ is moving with a velocity of $36 \mathrm{km} {\mathrm{h}}^{-1}$ towards a hill from which an echo is heard by the train driver. Velocity of sound in air is $330 \mathrm{m} {\mathrm{s}}^{-1}$.

A travelling wave is described by the equation $y\left(x,t\right)=\left[0.05\sin \left(8x-4t\right)\right] \mathrm{m}$. The velocity of the wave is:

[All the quantities are in SI unit]

The distance between two consecutive points with phase difference of $60°$ in a wave of frequency $500 \mathrm{Hz}$ is $6.0 \mathrm{m}$. The velocity with which wave is travelling is ______ $\mathrm{km} {\mathrm{s}}^{-1}$.

A train blowing a whistle of frequency $320 \mathrm{Hz}$ approaches an observer standing on the platform at a speed of $66 \mathrm{m} {\mathrm{s}}^{-1}$. The frequency observed by the observer will be (given speed of sound $=330 \mathrm{m} {\mathrm{s}}^{-1}$) ______ $\mathrm{Hz}$.

A person observes two moving trains, $A$ reaching the station and $B$ leaving the station with equal speed of $30 \mathrm{m} {\mathrm{s}}^{-1}$. If both trains emit sounds with frequency $300 \mathrm{Hz}$, (Speed of sound : $330 \mathrm{m} {\mathrm{s}}^{-1}$) approximate difference of frequencies heard by the person will be :

Two simple harmonic waves having equal amplitudes of $8 \mathrm{cm}$ and equal frequency of $10 \mathrm{Hz}$ are moving along the same direction. The resultant amplitude is also $8 \mathrm{cm}$. The phase difference between the individual waves is _____ degree.

For a solid rod, the Young's modulus of elasticity is $3.2\times {10}^{11} \mathrm{N} {\mathrm{m}}^{-2}$ and density is $8\times {10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$. The velocity of longitudinal wave in the rod will be

A steel wire with mass per unit length $7.0 \times {10}^{–3} \mathrm{kg} {\mathrm{m}}^{–1}$ is under tension of $70 \mathrm{N}$. The speed of transverse waves in the wire will be: