Question

The transverse displacement of a string (clamped at Its both ends) is given by y(x,t) = 0.06 sin\((\frac{2π}{3}x)\). cos(120πt) 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 x 10^-2 kg. 

Answer the following : 

1. Does the function represent a travelling wave or a stationary wave? 

2. Interpret the wave as a superposition of two waves travelling in opposite directions. What is the wavelength, frequency, and speed of each wave? 

3. Determine the tension in the string.

Answer 1

1. The function represents a stationary wave. 

2.

 

∴ λ = 3 m , f = 60 Hz, v = \(\frac{120π}{2π} \times 3\) 

= 180 ms^-1 for both waves. 

3. We know that T = µ v² where µ = mass per unit length of the string

\(\frac{3 \times 10^{-2}}{1.5m}\) = 2 × 10^-2 kgm^-1

∴ T = 2 × 10^-2 × 180² = 648 N