The wave described by y = 0.25 sin (10 2πx – 2πt), where x and y are in meters and t in second is a wave travelling along the:

Options

(a) negative x direction with frequency 1 Hz.
(b) positive x direction with frequency π Hz and wavelength λ = 0.2 m.
(c) positive x direction with frequency 1 Hz and wavelength λ = 0.2 m.
(d) negative x direction with amplitude 0.25 m and wavelength λ = 0.2 m.

Correct Answer:

positive x direction with frequency 1 Hz and wavelength λ = 0.2 m.

Explanation:

y = 0.25 sin (10 2πx – 2πt) Comparing this equation with the standard wave equation
y = a sin (kx – ?t) We get, k = 10π
⇒ 2π / λ = 10π ⇒ λ = 0.2 m.
? = 2π or, 2πv = 2π ⇒ v = 1 Hz.
The sign insider the bracket is negative, hence the wave travels in +ve x-direction.