A wave travelling in the +ve x-direction having displacement along y-direction as 1m, wavelength 2π and frequency 1 /π Hz is represented by

Options

(a) y = sin ( 2 πx – 2 πt )
(b) y = sin ( 10 πx – 20 πt )
(c) y = sin ( 2 πx + 2 πt )
(d) y = sin ( x – 2t )

Correct Answer:

y = sin ( x – 2t )

Explanation:

As Y = A sin (ωt – kx + ɸ)
ω = 2πf = 2π / π = 2 [f = 1/ π]
k = 2π / λ = 2π / 2π = 1 [ λ = 2π]
Therefore,
Y = 1 sin (2t – x + ɸ) [A = 1 m]