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

A car travelling at a speed of 54 kmph towards a wall sounds horn of frequency 400 Hz . The difference in the frequencies of two sounds, one received directly from the car and other reflected from the wall noticed by a person standing between the car and the wall is (speed of sound in air is $335 \mathrm{~m} / \mathrm{s}$ )