A man is watching two trains, one leaving and the other coming with equal speed of $4\,m/s$ . If they sound their whistles each of frequency $240\, Hz$ , the number of beats per sec heard by man will be equal to: (velocity of sound in air $= 320\, m/s$ )

A wave travelling in the $-ve\,\,z-$ direction having displacement along $x-$ direction as $1\,m,$ wavelength $\pi\, m$ and frequency at $\frac {1}{\pi }\,H_Z$ is represented by

A uniform string suspended vertically. A transverse pulse is created at the top most of the string. Then

Three sound waves of equal amplitudes have frequencies $(f-1 ), f, (f+ 1)$. They superpose to give beats. The number of beats produced per second will be:

Two pipes are each $50\,cm$ in length. One of them is closed at one end while the other is  both ends. The speed of sound in air is $340\,ms^{-1}.$ The frequency at which both the pipes can resonate is

Equation of a plane progressive wave is given by $y = 0.6\sin 2\pi \left( {t - \frac{x}{2}} \right)$. On reflection from a denser medium its amplitude becomes $2/3$ of the amplitude of the incident wave. The equation of the reflected wave is