A toy-car, blowing its horn, is moving with a steady speed of 5 m/s, away from a wall. An observer, towards whom the toy car is moving, is able to hear 5 beats per second. If the velocity of sound in air is 340 m/s, the frequency of the horn of the toy car is close to :

Two engines pass each other moving in opposite directions with uniform speed of 30 m/s. One of them is blowing a whistle of frequency 540 Hz. Calculate the frequency heard by driver of second engine before they pass each other. Speed of sound is 330 m/sec :

A uniform string of length $$20$$ $$m$$ is suspended from a rigid support. A short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the supports is :
(take $${\,\,g = 10m{s^{ - 2}}}$$ )

A pipe open at both ends has a fundamental frequency $$f$$ in air. The pipe is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column is now :