Question

If y = 0.02 sin (30x – 200t) (SI units), the frequency of the wave is

Answer 1

Answer:

31.831 Hz.

Explanation:

Given:

• $\rm y = 0.02\sin(30x-200 t).$

The vertical displacement of a wave is given in generalized form as

$\rm y = A\sin(kx -\omega t).$

where,

• A = amplitude of the displacement of the wave.
• k = wave number of the wave = $\dfrac{2\pi }{\lambda}.$
• $\lambda$ = wavelength of the wave.
• x = horizontal displacement of the wave.
• $\omega$ = angular frequency of the wave = $\rm 2\pi f$.
• f = frequency of the wave.
• t = time at which the displacement is calculated.

On comparing the generalized equation with the given equation of the displacement of the wave, we get,

$\rm A=0.02.\\k=30.\\\omega =200.$

therefore,

$\rm 2\pi f=200\\\\\Rightarrow f = \dfrac{200}{2\pi}=31.831\ Hz.$

It is the required frequency of the wave.