15.19 Explain why (or how):
(a) in a sound wave, a displacement node is a pressure antinode and vice versa?
(b) bats can ascertain distances, directions, nature, and sizes of the obstacles without any “eyes”?
(c) a violin note and sitar note may have the same frequency, yet we can distinguish between the two notes?
(d) solids can support both longitudinal and transverse waves, but only longitudinal waves can propagate in gases?
(e) the shape of a pulse gets distorted during propagation in a dispersive medium?
(a) A node is a point where the pressure is the maximum and the amplitude of vibration is the minimum. On the other hand, an antinode is a point where the pressure is the minimum and the amplitude of vibration is the maximum.
Therefore, a displacement node is nothing but a pressure antinode and vice versa.
(b) The ultrasonic sound waves, emitted by the bats, get reflected back towards them by the obstacles. A bat receives a reflected wave (frequency) and estimates the distance, direction, nature, and size of an obstacle with the help of its brain senses.
(c) The overtones produced by a sitar and a violin, and the strengths of these overtones, are different. Hence, one can distinguish between the notes produced by a sitar and a violin even if they have the same frequency of vibration.
(d) Solids have shear modulus. They can sustain shearing stress. Since fluids do not have any definite shape, they yield to shearing stress. The propagation of a transverse wave is such that it produces shearing stress in a medium. The propagation of such a wave is possible only in solids, and not in gases.
Both solids and fluids have their respective bulk moduli. They can sustain compressive stress. Hence, longitudinal waves can propagate through solids and fluids.
(e) A pulse is actually is a combination of waves having different wavelengths. These waves travel in a dispersive medium with different velocities, depending on the nature of the medium. This results in the distortion of the shape of a wave pulse.