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

Answer:

Frequency, f = 0.63 Hz

Period, T = 1.58 s

Speed of a wave, v = 1.34 m/s

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,

$\omega=2\pi f\\\\f=\dfrac{\omega}{2\pi}\\\\f=\dfrac{4}{2\pi}\\\\f=0.63\ Hz$

(ii) Period of wave is :

$T=\dfrac{1}{f}\\\\T=\dfrac{1}{0.63}\\\\T=1.58\ s$

(iii) Speed of a wave,

$v=\dfrac{\omega}{k}\\\\v=\dfrac{4}{3}\\\\v=1.34\ m/s$