Question

Find the wrong statement from the following about the equation of stationary wave given by Y = 0.04 cos(πx) sin(50 πt) m where t is in second. Then for the stationary wave.

Options

• Time period = 0.02 s

• Wavelength = 2 m

• Velocity= 50 m/s

• Amplitude = 0.02 m

Answer 1

Time period = 0.02 s

Explanation:

The displacement of a wave in term of time period is given by

y = A sin `[2pi ("t"/"T" - x/lambda)]`

This equation in terms of speed of wave (v), becomes y = A sin `[(2pi)/lambda ("vt" - x)]`

The given equation of wave is

Y = 0.04 cos(πx) sin(50 πt)

= 0.02 sin (50πt + πx) + 0.02 sin(50πt - πx)  ...[2sin A · cos B = sin (A + B) · (A - B)]

Thus, the given wave is the combination of two waves,

y₁ = 0.02 sin(50πt + πx)   ....(in -ve x- direction)

and y₂ = 0.02 sin(50πt - πx)   ....(in +ve x- direction)

Comparing them with the general equation of wave a sin (ωt + kx), we get

Amplitude, a = 0.02 m

Time period, T = `(2pi)/(50 pi) = 1/25` = 0.04 s

Wavelength, `lambda = (2pi)/pi` = 2 m

Velocity, v = `(50 pi xx lambda)/(2pi)`

`= 100/2` = 50 ms^-1

So, 1st option is wrong.