Question

A string of mass $0.1\,\text{kg$ is under a tension $1.6\,\text{N}$. The length of the string is $1\,\text{m}$. A transverse wave starts from one end of the string. The time taken by the wave to reach the other end is}

• A. $0.30\,\text{s}$
• B. $0.50\,\text{s}$
• C. $0.25\,\text{s}$
• D. $0.75\,\text{s}$

Hint:

Wave speed on a string increases with tension and decreases with mass per unit length.

Answer 1

The Correct Option is C

Step 1: Formula for speed of transverse wave.
\[ v = \sqrt{\frac{T}{\mu}} \] where $\mu$ is mass per unit length.

Step 2: Calculating mass per unit length.
\[ \mu = \frac{0.1}{1} = 0.1\,\text{kg m}^{-1} \]
Step 3: Calculating wave speed.
\[ v = \sqrt{\frac{1.6}{0.1}} = \sqrt{16} = 4\,\text{m s}^{-1} \]
Step 4: Time taken to travel length of string.
\[ t = \frac{L}{v} = \frac{1}{4} = 0.25\,\text{s} \]
Step 5: Conclusion.
The wave takes $0.25\,\text{s}$ to reach the other end.