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The transverse displacement of a string ...

The transverse displacement of a string (clamped at its both ends) is given by
`y(x, t) = 0.06 sin ((2 x)/(3) x) cos (120 pi t)`
where x and y are in m and t in s. The length of the string is 1.5 m and its mass is `3.0 xx 10^(-2) kg`.
Answer the following :
(a) Does the function represent a travelling wave or a stationary wave?
(b) Interpret the wave as a superposition of two waves travelling in opposite directions. What is the wavelength, frequency , and speed of each wave ?
(c ) Determine the tension in the string.

Text Solution

Verified by Experts

(a) Stationary wave (b) `l=3, n=60Hz, and v= 180 ms^(-1)` for each wave
(c ) 648N
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Knowledge Check

  • The displacement of a string is given by y (x,t) = 0.06 sin ((2pi x )/(3)) cos (120 pit). Where x and y are in m and t in s. The length of the string is 1.5 m and its mass is 3.0 xx 10 ^(-2) kg .

    A
    It represents a progressive wave of frequency 60 Hz.
    B
    It represents a stationary wave of frequency 60 Hz.
    C
    It is the result of superopostion of two waves of wavelength 3m, frequency 60 Hz each travelling with a speed of 180 m/s in opposite direction.
    D
    Amplitude of this wave is constant.

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  • A transverse harmonic wave on a string is described by y (x,t) =3.0 sin (36 t + 0.018 x + (pi)/(4)) where x and y are in cm and t is in s. The positive direction of r is from left to right.

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    The wave is travelling from right to left.
    B
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