Question

The equation y= 5 Sin (3x-4), where y is in millimeters,x is in metres and t is in seconds, represent a wave motion. Determine the (I) frequency (ii) period (III) speed of wave

Answer 1

(I)

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

(II)

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

(III)

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