Question

If the tension applied to a string is decreased by 36%, then the fundamental frequency of the transverse waves of the string is:

• A. Increases by 10%
• B. Decreases by 10%
• C. Increases by 20%
• D. Decreases by 20%

Hint:

The frequency of a string is proportional to the square root of the tension. Decreasing the tension decreases the frequency.

Answer 1

The Correct Option is D

Step 1:
The fundamental frequency of the transverse wave on a string is given by: $$f = \frac{1}{2L} \sqrt{\frac{T}{\mu}}$$ where $T$ is the tension, $L$ is the length, and $\mu$ is the mass per unit length of the string.
Step 2:
When the tension is decreased by 36%, the new tension $T'$ is $0.64T$. The new frequency is: $$f' = \frac{1}{2L} \sqrt{\frac{0.64T}{\mu}} = \frac{f}{\sqrt{0.64}} = \frac{f}{0.8}$$
Step 3:
The frequency decreases by 20%.