Question

The transverse displacement of a string (clamped at its two ends) is given by 

y(x,t) = 0.60 sin 2π/3 cos120 ωt.

where x, y are in m and t is 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 or a stationary wave? 

(b) Interpret the wave as a superposition of two waves travelling in opposite directions. What are the wavelength frequency and speed of propagation of each wave ? 

(c) Determine the tension in the string.

Answer 1

(a) The displacement which involves harmonic functions of x and t separately represents a stationary wave and the displacement, which is harmonic function of the form (vt ± x), represents a travelling wave. Hence, the equation given above represents a stationary wave.

(b) When a wave pulse y₁ = a sin 2π/λ(vt - x) travelling along x-axis is superimposed by the reflected pulse.

y₂ = -a sin 2π/λ(vt - x)  from the other end, a stationary wave is formed and is given by

(c) Velocity of transverse wave in a string is given by