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The transverse displacement y(x, t) of a...

The transverse displacement `y(x, t)` of a wave on a string is given by `y(x, t)= e ^(-(ax^(2) + bt^(2) + 2sqrt((ab))xt)`. This represents a :

A

Wave movinig in -ve `x` direction with speed `sqrt(b//a)`

B

Wave moving in + ve `x` direction with speed `sqrt(b//a)`

C

Standing wave of frequency `sqrt(b)`

D

Standing wave of frequency `(1)/(sqrt(b))`

Text Solution

Verified by Experts

The correct Answer is:
A
`y(x,t)=e^(-(sqrt(a)x+sqrt(b)t)^(2))`
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Knowledge Check

  • The transverse displacement of a string clamped at its both ends is given by y(x,t)=2sin((2pi)/3x)cos(100pit) where x and y are in cm and t is in s. Which of the following statements is correct?

    A
    All the points on the string between two consecutive nodes vibrate with same frequency, phase and amplitude.
    B
    All the points on the string between two consecutive nodes vibrate with same frequency and phase but different amplitude.
    C
    All the points on the string between two consecutive nodes vibrate with different frequency and phase but same amplitude.
    D
    All the points on the string between two consecutive nodes vibrate with different frequency, phase and amplitude

  • The transverse displacement of a string (clamped at its both ends ) is given by y(x,t)=0.06sin(2pix//3)cos(120pit). All the points on the string between two consecutive nodes vibrate with

    A
    same frequency
    B
    same phase
    C
    same energy
    D
    different amplitude

  • A transverse wave travelling on a stretched string is is represented by the equation y =(2)/((2x - 6.2t)^(2)) + 20 . Then ,

    A
    velocity of the wave is `3.1m//s`
    B
    amplitude of the wave is `0.1m`
    C
    frequency of the wave is `20 Hz`
    D
    wavelength of the wave is `1m`
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