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 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

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