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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:
(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.
Asked by Ramkumar Last Modified
Answer 
Shivam Sharma
(a) 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:
Hence, the given function represents a stationary wave.
(b) A wave travelling along the positive x-direction is given as:
The wave travelling along the negative x-direction is given as:
The superposition of these two waves yields:
The transverse displacement of the string is given as:
Comparing equations (i) and (ii), we have:
∴Wavelength, λ = 3 m
It is given that:
120π = 2πν
Frequency, ν = 60 Hz
Wave speed, v = νλ
= 60 × 3 = 180 m/s
(c) The velocity of a transverse wave travelling in a string is given by the relation:
Where,
Velocity of the transverse wave, v = 180 m/s
Mass of the string, m = 3.0 × 10–2 kg
Length of the string, l = 1.5 m
Mass per unit length of the string, 
Tension in the string = T
From equation (i), tension can be obtained as:
T = v2μ
= (180)2 × 2 × 10–2
= 648 N
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