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.​

Respuesta :

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 :

[tex]y = 5 \sin (3x - 4t)[/tex] ...(1)

y is in mm

x is in meters

t is in seconds

The general equation of a wave is given by :

[tex]y=A\sin(kx-\omega t)[/tex] ...(2)

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

[tex]k=3\\\\\omega=4[/tex]

Since,

[tex]\omega=2\pi f\\\\f=\dfrac{\omega}{2\pi}\\\\f=\dfrac{4}{2\pi}\\\\f=0.63\ Hz[/tex]

(ii) Period of wave is :

[tex]T=\dfrac{1}{f}\\\\T=\dfrac{1}{0.63}\\\\T=1.58\ s[/tex]

(iii) Speed of a wave,

[tex]v=\dfrac{\omega}{k}\\\\v=\dfrac{4}{3}\\\\v=1.34\ m/s[/tex]

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