Wave Mechanics Vibration Of String Question 30
Question: Two wires are in unison. If the tension in one of the wires is increased by 2%, 5 beats are produced per second. The initial frequency of each wire is
[MP PET 2002]
Options:
A) 200 Hz
B) 400 Hz
C) 500 Hz
D) 1000 Hz
Show Answer
Answer:
Correct Answer: C
Solution:
$ n\propto \sqrt{T} $
Therefore $ \frac{\Delta n}{n}=\frac{\Delta T}{2T} $ If tension increases by 2%, then frequency must increases by 1%.
If initial frequency $ n _{1}=n $ then final frequency n2 ? n1 = 5
Therefore $ \frac{101}{100}n-n=5 $
Therefore $ n=500Hz.
$ Short trick : If you can remember then apply following formula to solve such type of problems.
Initial frequency of each wire (n) $ =\frac{\text{(Number}\ of\ beats\ heard\ per\ \text{sec)}\times 200}{\text{(per}\ centage\ change\ in\ tension\ of\ the\ \text{wire)}} $ Here $ n=\frac{5\times 200}{2}=500Hz $
BETA
