The number of possible natural oscillations of air column in a pipe closed at one end of length $$85 \mathrm{~cm}$$ whose frequencies lie below $$1250 \mathrm{~Hz}$$ are (velocity of sound $$=340 \mathrm{~ms}^{-1}$$)

A tuning fork of unknown frequency produces 4 beats with tuning fork of frequency $$310 \mathrm{~Hz}$$. It gives the same number of beats on filing. The initial frequency of a tuning fork is

A string of length $$25 \mathrm{~cm}$$ and mass $$10^{-3} \mathrm{~kg}$$ is clamped at its ends. The tension in the string is $$2.5 \mathrm{~N}$$. The identical wave pulses are generated at one end and at regular interval of time, $$\Delta \mathrm{t}$$. The minimum value of $$\Delta \mathrm{t}$$, so that a constructive interference takes place between successive pulses is