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

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)

An air column, closed at one end open at the other, resonates with a tuning fork when the smallest length of the column is 50 cm. The next larger length of the column resonating with the same tuning fork is

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