Wave Mechanics Vibration Of String Question 45
Question: Two vibrating strings of the same material but lengths L and 2L have radii 2r and r respectively. They are stretched under the same tension. Both the strings vibrate in their fundamental modes, the one of length L with frequency n1 and the other with frequency n2. The ratio n1/n2 is given by
[IIT-JEE (Screening) 2000]
Options:
A) 2
B) 4
C) 8
D) 1
Show Answer
Answer:
Correct Answer: D
Solution:
Fundamental frequency $ n=\frac{1}{2l}\sqrt{\frac{T}{\pi r^{2}\rho }} $ where m = Mass per unit length of wire
Therefore $ n\propto =\frac{1}{lr}\Rightarrow \frac{n _{1}}{n _{2}}=\frac{r _{2}}{r _{1}}\times \frac{l _{2}}{l _{1}}=\frac{r}{2r}\times \frac{2L}{L}=\frac{1}{1} $
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