Question

The equation of a progressive wave can be given by y = 15 sin (660πt – 0.02πx) cm.

The frequency of the wave is:

(A) 330Hz

(B) 342Hz

(C) 365Hz

(D) 660Hz

Answer 1

A progressive wave is described as the onward propagation of a body's vibratory motion from one particle to the next particle in an elastic medium.

In a medium through which a wave moves, an equation can be developed to generally describe the displacement of a vibrating particle. Thus, each particle of a progressive wave performs simple harmonic motion of the same time and amplitude that varies from each other in phase.

For a wave function of time and space, the two expressions can be merged as y (x, t) =Asin(ωt−kx) and this is called the equation of a progressive wave. The minus sign is used to have a moving wavefront from left to right and t should be taken as positive with ωt≥ kx

Complete step by step answer:

Given: y = 15 sin (660πt – 0.02πx) cm

The general equation of a progressive wave is

y (x, t) =Asin(ωt−kx)

where y(x,t) gives the displacement of the elements of the string at a position x at any time t, A is the amplitude, k is the angular wave number and ω is the angular frequency.

ω=2πν

ν =$\frac {660\pi} {2\pi}$

ν =330Hz

Hence, the correct option is A.

Note: Progressive Wave Characteristics

(a) Each medium particle performs a vibration of its mean position. From one atom to another, the disruption continues onwards.

(b) Medium particles vibrate at the same amplitude in comparison to their mean location

(c) Each successive particle of the medium travels along the propagation of the wave in a motion identical to that of its ancestor, but later in time.

(d) Every particle's phase shifts from 0 to 2π.