D. C. Pandey Solutions for Chapter: Wave Motion, Exercise 1: Objective Problems

A wave of frequency $100 \mathrm{Hz}$ is sent along a string towards a fixed end. When this wave travels back, after reflection, a node is formed at a distance of $10 \mathrm{cm}$ from the fixed end of the string. The speeds of incident (and reflected) waves are

The resultant amplitude due to superposition of two harmonic waves expressed by $y=a\sin \left(\mathrm{\omega }t-kx\right)$ and $y=a\cos \left(kx-\mathrm{\omega }t\right)$ will be

In a sinusoidal wave, the minimum time required for a particular point to move from maximum displacement to zero displacement is $0.17 \mathrm{s}$. The frequency of the wave is

In a medium, a transverse progressive wave is travelling, the phase difference between two points with separation of $1.25 \mathrm{cm}$ is $\left(\frac{\pi }{3}\right)$. If the frequency of a wave is $1000 \mathrm{Hz}\text{,}$ its velocity will be

Assertion: If a stretched wire fixed at both ends is vibrating in its second overtone mode, then the total number of nodes and antinodes are four each.

Reason: Number of antinodes is equal to the number of loops.

Assertion: Transverse waves cannot travel in the gaseous medium.

Reason: Gaseous medium does not have a modulus of rigidity.

Assertion: A wire is stretched and then fixed at two ends. The wavelength of second overtone mode is $\frac{2}{3}\mathrm{rd}$ of the wavelength of first overtone mode.

Reason: Frequency of second overtone mode is $\frac{3}{2}$ times the frequency of first overtone mode.

In sine wave, minimum distance between $2$ particles having same speed is always