A train approaching a railway plateform with a speed of  $20\,\,m\,s^{-1}$ starts blowing the whistle speed of sound in air is $340\,\,ms^{-1}.$ If frequency of the emitted sound from the whistle is  $640\,\,Hz,$  the frequency of sound as heard by person standing on the platform is .... $Hz$

An organ pipe $P_1$ closed at one end vibrating in its first overtone. Another pipe $P_2$  open at both ends is vibrating in its third overtone. They are in a resonance with a  given tuning fork. The ratio of the length of $P_1$ to that of $P_2$ is

A string fixed at one end is vibrating in its second overtone. The length of the string is $10\  cm$ and maximum amplitude of vibration of particles of the string is $2\ mm$ . Then the amplitude of the particle at $9\ cm$ from the open end is

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

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

The equation of transverse wave in stretched string is $y = 5\,\sin \,2\pi \left[ {\frac{t}{{0.04}} - \frac{x}{{50}}} \right]$ Where distances are in cm and time in second. The wavelength of wave is .... $cm$