Question

A sinusoidal wave has the following wave function: y(x,t) = (2.5 m) sin((3.0 m ) x - (24 s-')t + Tt/2] What is the frequency of this wave? (a) 0.48 Hz, (b) 3.0 Hz, (c) 3.8 Hz, (d) 12 Hz, (e) 24 Hz.

Answer 1

Frequency of the wave is 3.8 hertz.

Step-by-step explanation:

It is given that, the sinusoidal wave has following wave equation as :

`y(x,t)=(2.5\ m)sin[(3\ m^(-1))x-(24\ s^(-1))t+\pi/2]`

The general equation for the sinusoidal wave is :

`y=A\ sin(kx-\omega t+\phi)`

Where

A is the amplitude

k is the constant

`\omega` is the angular frequency

`\phi` is the phase difference

Since,
`\omega=24\ s^(-1)`

`2\pi f=24`

`f=(24)/(2\pi)=3.81\ Hz`

or

f = 3.8 Hz

So, the frequency of the wave is 3.8 hertz. Hence, this is the required solution.