First slide

Stationary waves

Question

The frequency of a stretched uniform wire under tension is in resonance with the fundamental frequency of a closed tube. If the tension in the wire is increased by 8 N, it is in resonance with the first overtone of the closed tube. The initial tension in the wire is

Moderate

A

1 N
B

4 N
C

8 N
D

16 N

Solution

According to problem
$\frac{1}{2 L} \sqrt{\frac{T}{m}} = \frac{v}{4 L}$ …..(i)
and $\frac{1}{2 L} \sqrt{\frac{T + 8}{m}} = \frac{3 v}{4 L}$ ..…(ii)
Dividing equation (i) and (ii), $\sqrt{\frac{T}{T + 8}} = \frac{1}{3} \Rightarrow T = 1 N$

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