Question

The equation y = 5 Sin (3x - 4t), where

y is in millimeters, x is in metres and t
is in seconds, represents a wave motion.
Determine the (i) frequency (ii) period
(iii) speed of the wave.​

Answer 1

Frequency, f = 0.63 Hz

Period, T = 1.58 s

Speed of a wave, v = 1.34 m/s

Step-by-step explanation:

The equation of a wave is given by :

`y = 5 \sin (3x - 4t)` ...(1)

y is in mm

x is in meters

t is in seconds

The general equation of a wave is given by :

`y=A\sin(kx-\omega t)` ...(2)

(i) Compare equation (1) and (2) we get :

`k=3\\\\\omega=4`

Since,

`\omega=2\pi f\\\\f=(\omega)/(2\pi)\\\\f=(4)/(2\pi)\\\\f=0.63\ Hz`

(ii) Period of wave is :

`T=(1)/(f)\\\\T=(1)/(0.63)\\\\T=1.58\ s`

(iii) Speed of a wave,

`v=(\omega)/(k)\\\\v=(4)/(3)\\\\v=1.34\ m/s`