Question

The equation y= 5 sin (3x-4) where y is in millimetres,x is in metres and t is in seconds, represent a a wave motion. Determine
a) Frequency (b) Period (c) speed of the wave

Answer 1

The wave equation can be written as follows:

$$y=Asin(kx-\omega t),$$

here, $A$ is the amplitude of the wave, $k$ is the wavenumber, $\omega$ is the angular frequency of the wave.

By the definition of the question, we have:

$$y=5sin(3x-4t).$$

From this equation we can get the angular frequency and wavenumber:

$$\omega=4\ s^{-1}, k=3\ m^{-1}.$$

a) We can find the frequency of the wave from the formula:

$$f=\dfrac{\omega}{2\pi}=\dfrac{4\ s^{-1}}{2\pi} = 0.64\ Hz.$$

b) We can find the period of the wave from the formula:

$$f=\dfrac{1}{T},$$

here, $T$ is the period of the wave.

Then, we get:

$$T=\dfrac{1}{f}=\dfrac{1}{0.64\ Hz}=1.56\ s.$$

c) We can find the speed of the wave from the formula:

$$v=\dfrac{\omega}{k}=\dfrac{4\ s^{-1}}{3\ m^{-1}}=1.33\ ms^{-1}.$$

Answer:

a) $f=0.64\ Hz.$

b) $T=1.56\ s.$

c) $v=1.33\ ms^{-1}.$