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 :

A train is moving on a straight track with speed $$20\,m{s^{ - 1}}.$$ It is blowing its whistle at the frequency of $$1000$$ $$Hz$$. The percentage change in the frequency heard by a person standing near the track as the train passes him is (speed of sound $$ = 320\,m{s^{ - 1}}$$) close to :

A pipe of length $$85$$ $$cm$$ is closed from one end. Find the number of possible natural oscillations of air column in the pipe whose frequencies lie below $$1250$$ $$Hz$$. The velocity of sound in air is $$340$$ $$m/s$$.