Question

A steel wire of length 81 cm has a mass of $5 \times 10^{-3}$ kg. If the wire is under a tension of 50 N, then the speed of transverse waves on the wire is:

• A. 100 m s$^{-1}$
• B. 105 m s$^{-1}$
• C. 90 m s$^{-1}$
• D. 60 m s$^{-1}$

Hint:

Always convert all measurements to SI units before applying the formula. Use \( v = \sqrt{T/\mu} \) for speed of transverse waves on a stretched string.

Answer 1

The Correct Option is C

Step 1: Use the formula for wave speed on a stretched string 
\[ v = \sqrt{\frac{T}{\mu}} \] where \( T = \) tension and \( \mu = \) mass per unit length. 
Step 2: Convert length and compute linear mass density 
Length \( L = 81 \, \text{cm} = 0.81 \, \text{m} \) 
Mass \( m = 5 \times 10^{-3} \, \text{kg} \) 
\[ \mu = \frac{m}{L} = \frac{5 \times 10^{-3}}{0.81} \approx 6.17 \times 10^{-3} \, \text{kg/m} \] Step 3: Calculate wave speed 
\[ v = \sqrt{\frac{50}{6.17 \times 10^{-3}}} \approx \sqrt{8100} = 90 \, \text{m/s} \]