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.

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.​

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RobertKer 4 years 2021-09-04T23:30:43+00:00 1 Answers 150 views 0

Answers ( )

  1. thienan
    0
    2021-09-04T23:31:52+00:00
    Reply

    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

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