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.