Question

Which of the following is the law of vibrating string?

• A. The fundamental frequency is directly proportional to the square of the tension in the string.
• B. The fundamental frequency of stretched string is inversely proportional to the square root of the tension in the string.
• C. The fundamental frequency is inversely proportional to the square root of the linear mass density.
• D. Both (a) and (c)

Answer 1

The correct option is C

The fundamental frequency is inversely proportional to the square root of the linear mass density.

Correct option is C: The fundamental frequency is inversely proportional to the square root of the linear mass density.

There are main three laws for stretch of string:

1. Law of length: The fundamental frequency $\left(n\right)$ is inversely proportional to length $\left(l\right)$. $n\propto \frac{1}{l}$
2. Law of tension: The fundamental frequency $\left(n\right)$ is directly proportional to square root of tension. $n\propto \sqrt{T}$
3. Law of mass: The fundamental frequency $\left(n\right)$ is inversely proportional to square root of mass density. $n\propto \frac{1}{\sqrt{\mu }}$

Hence, option C is the law of vibrating string.