During propagation of a plane progressive mechanical wave
A. All the particles are vibrating in the same phase.

B. Amplitude of all the particles is equal.

C. Particles of the medium executes S.H.M.

D. Wave velocity depends upon the nature of the medium.

One end of a long string of linear mass density 8.0 × 10–3 kg m^–1 is connected to an electrically driven tuning fork of frequency 256 Hz. The other end passes over a pulley and is tied to a pan containing a mass of 90 kg. The pulley end absorbs all the incoming energy so that reflected waves at this end have negligible amplitude. At t = 0, the left end (fork end) of the string x = 0 has zero transverse displacement (y = 0) and is moving along positive y-direction. The amplitude of the wave is 5.0 cm. Write down the transverse displacement y as function of x and t that describes the wave on the string.

Explain why (or how):

the shape of a pulse gets distorted during propagation in a dispersive medium.

Given below are some functions of x and t to represent the displacement (transverse or longitudinal) of an elastic wave. State which of these represent (i) a travelling wave, (ii) a stationary wave or (iii) none at all:

(a) y = 2 cos (3x) sin (10t)

(b)

(c) y = 3 sin (5x – 0.5t) + 4 cos (5x – 0.5t)

(d) y = cos x sin t + cos 2x sin 2t

Explain why (or how):

solids can support both longitudinal and transverse waves, but only longitudinal waves can propagate in gases, and

Explain why (or how):

bats can ascertain distances, directions, nature, and sizes of the obstacles without any “eyes”,

A travelling harmonic wave on a string is described by

y(x, t) = 7.5 sin (0.0050x + 12t + π/4)

(a) what are the displacement and velocity of oscillation of a point at

x = 1 cm, and t = 1 s? Is this velocity equal to the velocity of wave propagation?

(b) Locate the points of the string which have the same transverse displacements and velocity as the x = 1 cm point at t = 2 s, 5 s and 11 s.

Explain why (or how):

in a sound wave, a displacement node is a pressure antinode and vice versa,

For the harmonic travelling wave y = 2 cos 2π (10t–0.0080x + 3.5) where x and y are in cm and t is second. What is the phase difference between the oscillatory motion at two points separated by a distance of,

(a) 4 m

(b) 0.5 m

(c)

(d) (at a given instant of time)

(e) What is the phase difference between the oscillation of a particle located at x = 100cm, at t = T s and t = 5 s?

In the given progressive wave y = 5 sin (100πt – 0.4πx) where y and x are in m, t is in s. What is the

(a) amplitude

(b) wave length

(c) frequency

(d) wave velocity

(e) particle velocity amplitude.

Given below are some functions of x and t to represent the displacement of an elastic wave.

(a) y = 5 cos (4x) sin (20t)

(b) y = 4 sin (5x – t/2) + 3 cos (5x – t/2)

(c) y = 10 cos [(252 – 250) πt ] cos [(252+250)πt ]

(d) y = 100 cos (100πt + 0.5x)