A uniform string is vibrating with a fundamental frequency 'f'. The new frequency, if radius and length both are doubled would be

Question

A uniform string is vibrating with a fundamental frequency 'f'. The new frequency, if radius and length both are doubled would be (A) 2f (B) 3f (C) (f/4) (D) (f/3)

Tardigrade Admin · Accepted Answer

Fundamental frequency of a vibrating string is expressed as

f = \frac{1}{2 L} \frac{T}{μ} = \frac{1}{L D} \frac{T}{π ρ}

where, D = diameter of string

ρ

= density of the material of string
As length L and radius are doubled, the new frequency

f^{'} = \frac{1}{( 2 L ) ( 2 D )} \frac{T}{π ρ} = \frac{1}{4} f

Q. A uniform string is vibrating with a fundamental frequency $^{'} f^{'}$ . The new frequency, if radius and length both are doubled would be

$2 f$

$3 f$

$\frac{f}{4}$

$\frac{f}{3}$

Q. A uniform string is vibrating with a fundamental frequency ′f′. The new frequency, if radius and length both are doubled would be

2f

3f

4f​

3f​

Fundamental frequency of a vibrating string is expressed as f=2L1​μT​​=LD1​πρT​​ where, D = diameter of string ρ = density of the material of string As length L and radius are doubled, the new frequency f′=(2L)(2D)1​πρT​​=41​f

Q. A uniform string is vibrating with a fundamental frequency $^{'} f^{'}$ . The new frequency, if radius and length both are doubled would be

$2 f$

$3 f$

$\frac{f}{4}$

$\frac{f}{3}$