Three sound waves of equal amplitudes have frequencies (n $$-$$ 1), n, (n + 1). They superimpose to give beats. The number of beats produced per second will be

The second overtone of an open organ pipe has the same frquency as the first overtone of a closed pipe L metre long. The length of the open pipe will be

A siren emitting a sound of frequency 800 Hz moves away from an observer towards a cliff at a speed of 15 m s^$$-$$1. Then, the frequency of sound that the observer hears in the echo reflected from the cliff is

(Take velocity of sound in air = 330 m s^$$-$$1)

A uniform rope of length L and mass m₁ hangs vertically from a rigid support. A block of mass m₂ is attached to the free end of the rope. A transverse pulse of wavelength $$\lambda $$₁ is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is $$\lambda $$₂. The ratio $$\lambda $$₂/$$\lambda $$₁ is