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]