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A wave pulse moving along the x axis is ...

A wave pulse moving along the `x` axis is represented by the wave funcation
`y(x, t) = (2)/((x - 3t)^(2) + 1)`
where `x` and `y` are measured in `cm` and `t` is in seconds.
`(i)` in which direction is the wave moving ?
`(ii)` Find speed of the wave.
`(iii)` Plot the waveform at `t = 0, t = 2s`.

Text Solution

Verified by Experts

The correct Answer is:
(i) Positive `xa` , (ii) `3 cm//s`.
`y = (2)/((x-3t)^(2) + 1)`
`(i)` As wave is moving in `+ve x` direction because
`y = (x, t) = f(t - x//AA) = f//v(vt - x)`
`(ii)` Now `x - vt` is concerened with `x - 3t`
`:. V = 3 cm//sec`.
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Knowledge Check

  • A wave is represented by the equation, y = 0.1 sin (60 t + 2x) , where x and y are in metres and t is in seconds. This represents a wave

    A
    travelling with a speed of `(1)/(30)` m/s, in the negative x direction
    B
    travelling with a speed of 30 m/s, in the positive x direction
    C
    of wavelength `30pi` metre
    D
    of frequency `((30)/(pi))` hertz

  • The wave function of a pulse is given by y=(5)/((4x+6t)^(2)) , where x and y are in metre and t is in second . The velocity of pulse is

    A
    `2m//s`
    B
    `6m//s`
    C
    `1.5 m//s`
    D
    `3m//s `

  • y(x,t)=(0.8)/((4x+5t)^(2)+5) represents a moving pulse where x and y are in meter and t in seconds. Then

    A
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    B
    In two seconds it will travel a distance of 2.5 m
    C
    It's maximum displacement is 0.16 m
    D
    It's a symmetric pulse.