Given below are some examples of wave motion. State in each case if the wave motion is transverse, longitudinal or a combination of both:
(a) Motion of a kink in a longitudinal spring produced by displacing one end of the spring sideways.
(b) Waves produced in a cylinder containing a liquid by moving its piston back and forth.
(c) Waves produced by a motorboat sailing in water.
(d) Ultrasonic waves in air produced by a vibrating quartz crystal.

What do you mean by interference of waves? Distinguish between constructive and destructive inerference. Standing waves are produced by the superposition of two waves y₁ = 0.05 sin(3ㅠt - 2x) and y₂ = 0.05 sin(3ㅠt + 2x) where y and x are measured in metres and t in seconds. Find the amplitude of a particle at x = 0.5 m.

What are the characteristics of stationary waves? Distinguish between stationary waves and progressive waves.

Discuss the various factors influencing velocity of sound. A sonometer wire of length 110 cm is stretched with a tension T and fixed at its ends. The wire is divided into three segments by placing two bridges beloui it. Where should the bridges be placed so that the fundamental frequencies of the segments are in the ratio 1 : 2 : 3?

What do you understand by beat? Explain beats analytically.

A metallic rod of length 1m is rigidly clamped at its midpoint. Longitudinal stationary waves are set up in the rod in such a way that there are two nodes on either side of the midpoint. The amplitude of an antinode is 2 x 10^-6 m. Write the equation of motion at a point 2 cm from the midpoint and those of the constituent waves in the rod. (Young's modulus = 2 x 10¹¹ Nm^-2 and density = 8000 kg m^-3)

The amplitude of a wave disturbed propagating in the positive x direction is given by \(y=\frac{1}{1+x^{2}}\) at t = 0 and \(y=\frac{1}{[1+(x-1)^{2}]}\) at t=2s where x and y in metre. The shape of disturbance does not change during the propagation. What is the velocity of the wave?