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 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 $$340$$ $$m/s$$.

A sonometer wire of length $$1.5$$ $$m$$ is made of steel. The tension in it produces an elastic strain of $$1\% $$. What is the fundamental frequency of steel if density and elasticity of steel are $$7.7 \times {10^3}\,kg/{m^3}$$ and $$2.2 \times {10^{11}}\,N/{m^2}$$ respectively ?