A sonometer wire supports a 4 kg load and vibrates in fundamental mode with a tuning fork of frequency 416 Hz. The length of the wire between the bridges is now doubled. In order to maintain fundamental mode, the load should be changed to

Question

A sonometer wire supports a 4 kg load and vibrates in fundamental mode with a tuning fork of frequency 416 Hz. The length of the wire between the bridges is now doubled. In order to maintain fundamental mode, the load should be changed to (A) 1 kg (B) 2 kg (C) 8 kg (D) 16 kg

Tardigrade Admin · Accepted Answer

For a sonometer, v text fundamental =(1/2 l) √(T/μ) To maintain the fundamental mode, on doubling the length, tension must be quadrupled.

Q. A sonometer wire supports a 4 kg load and vibrates in fundamental mode with a tuning fork of frequency $416 Hz$ . The length of the wire between the bridges is now doubled. In order to maintain fundamental mode, the load should be changed to

1 kg

2 kg

8 kg

16 kg

For a sonometer, $v_{fundamental} = \frac{1}{2 l} \frac{T}{μ}$
To maintain the fundamental mode, on doubling the length, tension must be quadrupled.

Q. A sonometer wire supports a 4 kg load and vibrates in fundamental mode with a tuning fork of frequency 416Hz. The length of the wire between the bridges is now doubled. In order to maintain fundamental mode, the load should be changed to