H C Verma Solutions for Chapter: Wave Motion and Waves on a String, Exercise 1: QUESTIONS FOR SHORT ANSWER

You are walking along a seashore and a mild wind is blowing. Is the motion of air a wave motion?

The radio and TV program, telecast at the studio, reach our antenna by wave motion. Is it a mechanical wave or non-mechanical?

A wave is represented by an equation, $y=c_1\sin \left(c_{2}x+c_{3}t\right).$ In which direction is the wave going? Assume that $c_1,c_2$ and $c_3$ are all positive.

Show that the particle speed can never be equal to the wave speed in a sine wave if the amplitude is less than wavelength divided by $2\pi$.

Two wave pulses identical in shape but inverted with respect to each other are produced at the two ends of a stretched string. At an instant when the pulses reach the middle, the string becomes completely straight. What happens to the energy of the two pulses?

Show that for a wave travelling on a string,

$\frac{y_{\max }}{v_{\max }}=\frac{v_{\max }}{a_{\max }}$,

where, the symbols have usual meanings. Can we use componendo and dividendo taught in algebra to write

$\frac{y_{\max }+v_{\max }}{y_{\max }-v_{\max }}=\frac{v_{\max }+a_{\max }}{v_{\max }-a_{\max }}$ ?

What is the smallest positive phase constant which is equivalent to $7.5\pi$?

A string clamped at both ends vibrates in its fundamental mode. Is there any position (except the ends) on the string which can be touched without disturbing the motion? What if the string vibrates in its first overtone?