Wave Mechanics Question 655
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
Options:
A) 1 kg
B) 2 kg
C) 4 kg
D) 16 kg
Show Answer
Answer:
Correct Answer: D
Solution:
[d] Load supported by sonometer wire = 4 kg Tension in sonometer wire = 4 g If $ \mu $ = mass per unit length then frequency $ v=\frac{1}{21}\sqrt{\frac{T}{\mu }} $
$ \Rightarrow 416=\frac{1}{21}\sqrt{\frac{4g}{\mu }} $ When length is doubled, i.e., $ l’=2l $ Let new load =L As, $ v’=v $
$ \
Therefore \frac{1}{2l’}\sqrt{\frac{Lg}{\mu }}=\frac{1}{2l}\sqrt{\frac{4g}{\mu }} $
$ \Rightarrow ,\frac{1}{4l}\sqrt{\frac{Lg}{\mu }}=\frac{1}{2l}\sqrt{\frac{4g}{\mu }} $
$ \Rightarrow \sqrt{L}=2\times 2\Rightarrow L=16kg $
BETA
