A sonometer wire $$49 \mathrm{~cm}$$ long is in unison with a tuning fork of frequency '$$n$$'. If the length of the wire is decreased by $$1 \mathrm{~cm}$$ and it is vibrated with the same tuning fork, 6 beats are heard per second. The value of '$$n$$' is

A source of sound is moving towards a stationary observer with $$\left(\frac{1}{10}\right)^{\text {th }}$$ the of the speed of sound. The ratio of apparent to real frequency is

A string is stretched between two rigid supports separated by $$75 \mathrm{~cm}$$. There are no resonant frequencies between $$420 \mathrm{~Hz}$$ and $$315 \mathrm{~Hz}$$. The lowest resonant frequency for the string is

A progressive wave is given by, $$\mathrm{Y}=12 \sin (5 \mathrm{t}-4 \mathrm{x})$$. On this wave, how far away are the two points having a phase difference of $$90^{\circ}$$ ?