The equation of a wave is given by, y = 2 sin (3x - t/4). The time period of the wave is :

CONCEPT:

The general equation of wave motion is given by:

y =  Asin (kx - ωt)

where A = amplitude, ω = angular frequency, k = angular wavenumber, t = time, and x is position

• Wavelength (λ): Distance between two nearest particles vibrating in the same phase.
• Frequency (f): Number of vibrations complete by a particle in one second.
• Time Period (T): Time taken by the wave to travel a distance equal to one wavelength.
• Amplitude (A): Maximum displacement of vibrating particles from the mean position.

The relationship between frequency (f), wavelength (λ), and velocity (v) of a wave is given by:

f × λ = v 

CALCULATION:

Given that:

y = 2 sin (3x - t/4)

By comparing above equation with the given standard equation we get,

A = 2; ω = 1/4 rad/s; k = 3 rad/m

We know that ω = 2πf and f = 1/T

ω = 2π/T

T = 2π/ω

T = 2π × (4/1) = 25.13 s

• Hence option 2 is correct