The difference between the fundamental frequencies of an open pipe and a closed pipe of same length is 100 Hz . The difference between the frequencies of the second harmonic of the open pipe and the third harmonic of the closed pipe is

The displacement equations of sound waves produced by two sources are given by $y_1=5 \sin 400 \pi t$ and $y_2=8 \sin 408 \pi t$, where $t$ is time in seconds. If the waves are produced simultaneously, the number of beats produced per minute is

A boy standing on a platform observes the frequency of a train horn as it passes by. The change in the frequency noticed as the train approaches and recedes him with a velocity of 108 kmph is (speed of sound in air $=330 \mathrm{~ms}^{-1}$ )

If three sources of sound of frequencies $(n-1), n$ and $(n+1)$ are vibrated together, the number of beats produced and heard per second respectively are