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

Answer:

Frequency of the wave is 3.8 hertz.

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, $\omega=24\ s^{-1}$

$2\pi f=24$

$f=\dfrac{24}{2\pi}=3.81\ Hz$

or

f = 3.8 Hz

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