First slide

Standing waves

Question

A wire of length l having tension T and radius r vibrates with fundamental frequency f. Another wire of the same metal with length 2l having tension 2T and radius 2 r will vibrate with fundamental frequency:

Moderate

A

f
B

2f
C

$\frac{f}{2 \sqrt{2}}$
D

$\frac{f}{2} \sqrt{2}$

Solution

$f = \frac{1}{2 l} \sqrt{\frac{T}{μ}}$
If radius is doubled and length is doubled, mass per unit length will become four times.
Hence $f = \frac{1}{2 \times 2 l} \sqrt{\frac{2 T}{4 μ}} = \frac{f}{2 \sqrt{2}}$

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