Question

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

Answer 1

31.831 Hz.

Step-by-step 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 =
  `(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 = (200)/(2\pi)=31.831\ Hz.`

It is the required frequency of the wave.