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) Does the function represent a travelling wave or a stationary wave? - Physics

Numerical

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.

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.

Concept: Displacement Relation for a Progressive Wave
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APPEARS IN

NCERT Class 11 Physics
Chapter 15 Waves
Exercises | Q 11.1 | Page 388