Four tuning forks of frequencies $200,201, 204$ and $206\, Hz$ are sounded together.  The beat frequency will be

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 $= 320\, m/s$ )

The diagram shows snapshot of a wave at time $t = 0$. The particle at $x = x_1$ is moving upward at that instant. Direction of propagation of wave is

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

Two vibrating strings of the same material but lengths $L$ and $2L$ have radii $2r$ and $r$ respectively. They are stretched under the same tension . Both the strings vibrate in their fundamental modes, the one of length $L$ with frequency $f_1$ and the other with frequency $f_2$. The ratio $\frac{f_1}{f_2}$ is given by

A train whistling at constant frequency is moving towards a station at a constant speed $V$. The train goes past a stationary observer on the station. The frequency $n'$ of the sound as heard by the observer is plotted as a function of time $t (Fig.)$ . Identify the expected curve