Question

The wave number (k) and the angular frequency of a wave are 6.2rad/m and 12rad/s respectively. Which of the followings could be the equation of the wave?

a. 8sin(12x-6.2t)
b. 8sin(6.2x-12t)
c. 12 sin (6.2x-8t)
d. all of the above

Answer 1

B.
`8sin(6.2x-12t)`

Step-by-step explanation:

The general equation of a wave is expressed as
`y = Asin(kx-\omega t)`

A is the amplitude of the wave

k is the wave number and it is expressed as
`k =(2\pi)/(\lambda)`

`\omega` is the angular frequency expressed as
`\omega = 2\pi f`

`\lambda` is the wavelength and f is the angular frequency

Given k = 6.2rad/m and
`\omega = 12rad/s`

On substituting this value into the general wave equation;

`y = Asin(kx-\omega t)\\y = Asin(6.2x-12t)`

From the expression gotten, the only equation that could be the equation of the wave is
`y = 8sin(6.2x-12t)`