A stationary tuning fork is in resonance with an air column in a pipe. If the tuning fork is moved with a speed of 2 ms⁻¹ in front of the open end of the pipe and parallel to it, the length of the pipe should be changed for the resonance to occur with the moving tuning fork. If the speed of sound in air is 320 ms⁻¹, the smallest value of the percentage change required in the length of the pipe is ____________.

A train S1, moving with a uniform velocity of 108 km/h, approaches another train S2 standing on a platform. An observer O moves with a uniform velocity of 36 km/h towards S2, as shown in figure.



Both the trains are blowing whistles of same frequency 120 Hz. When O is 600 m away from S2 and distance between S1 and S2 is 800 m, the number of beats heard by O is ............ . [Speed of the sound = 330 m/s ............ .]

Two men are walking along a horizontal straight line in the same direction. The man in front walks at a speed $$1.0\,m{s^{ - 1}}$$ and the man behind walks at a speed $$2.0\,m{s^{ - 1}}.$$ A third man in standing at a height $$12$$ $$m$$ above the same horizontal line such that all three men are in a vertical plane. The two walking men are blowing identical whistles which emit a sound of frequency $$1430$$ $$Hz$$. The speed of sound in air is $$330\,m{s^{ - 1}}.$$ At the instant, when the moving men are $$10$$ $$m$$ apart, the stationary man is equidistant from them. The frequency of beats in $$Hz,$$ heard by the stationary man at this instant, is _____________.

A stationary source emits sound of frequency $${f_0} = 492\,Hz.$$ The sound is reflected by a large car approaching the source with a speed of $$2\,m{s^{ - 1.}}$$ The reflected signal is received by the source and superposed with the original.

What will be the beat frequency of the resulting signal in $$Hz$$? (Given that the speed of sound in air is $$330\,m{s^{ - 1}}$$ and the car reflects the sound at the frequency it has received).