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Question
The transverse displacement of a string (clamped at its both ends) is given by
y(x, t) = 0.06 sin `2/3` x cos (120 πt)
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 × 10-2 kg.
Answer the following:
Does the function represent a travelling wave or a stationary wave?
Solution 1
The given equation is y(x, t) = 0.06 sin `(2π)/3 xx` cos 120 πt …(1)
As the equation involves harmonic functions of x and t separately, it represents a stationary wave.
Solution 2
The general equation representing a stationary wave is given by the displacement function:
y (x, t) = 2a sin kx cos ωt
This equation is similar to the given equation:
`"y"(x, "t") = 0.06 sin (2/3 x )x cos(120 pi "t")`
Hence, the given function represents a stationary wave.
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