Question

A string of length 3 m and mass 0.035 kg is stretched with a tension of 50 N. The speed of the wave on the string is:

• A. 18.6 m/s
• B. 15.4 m/s
• C. 16.2 m/s
• D. 14.4 m/s

Hint:

The speed of a wave on a string depends on the tension and the linear mass density of the string.

Answer 1

The Correct Option is B

Step 1: Use the wave speed formula.
The speed \( v \) of a wave on a string is given by: \[ v = \sqrt{\frac{T}{\mu}} \] where \( T \) is the tension and \( \mu \) is the linear mass density (\( \mu = \frac{m}{L} \)).

Step 2: Apply the values.
Given \( T = 50 \, \text{N} \), \( m = 0.035 \, \text{kg} \), and \( L = 3 \, \text{m} \), we find: \[ \mu = \frac{0.035}{3} = 0.01167 \, \text{kg/m} \] Substituting into the formula for \( v \), we get: \[ v = \sqrt{\frac{50}{0.01167}} = 15.4 \, \text{m/s} \]