Question

A string is stretched between two rigid supports. It vibrates with fundamental frequency f. If it is replaced with another wire whose radius and length are double, the new frequency for same tension is 1. f/2 , 2. f/4, 3. f/8, 4. f

Answer 1

Answer:

2

We know that

$f \: \: \: \: \alpha \: \: \: \frac{1}{l \sqrt{m} }$

Where

l is length and m is mass per unit length .

When radius is doubled mass per unit length will increase 4 times . ( Area is proportional to square of radius )

$m = \frac{ M}{l} = \frac{ \rho \times \pi {r}^{2} l}{l}$

So

$f ' = \frac{f}{2 \sqrt{4} } = \frac{f}{4}$