### Waves - Result Question 51

#### 53. A stretched string resonates with tuning fork frequency $512 Hz$ when length of the string is $0.5 m$. The length of the string required to vibrate resonantly with a tuning fork of frequency $256 Hz$ would be

[1993]

(a) $0.25 m$

(b) $0.5 m$

(c) $1 m$

(d) $2 m$

## Show Answer

#### Answer:

Correct Answer: 53. (d)

Solution:

- (d) $f=\frac{1}{2 l}[\frac{T}{\mu}]^{\frac{1}{2}}$. When $f$ is halved, the length is doubled.