First slide

Stationary waves

Question

Two similar sonometer wires given fundamental frequencies of 500Hz. These have same tensions. By what amount the tension be increased in one wire so that the two wires produce 5 beats/sec

Moderate

A

1%
B

2%
C

3%
D

4%

Solution

To produce 5 beats/sec. Frequency of one wire should be increase up to 505 Hz. i.e. increment of 1% in basic frequency.
$n \propto \sqrt{T} or T \propto n^{2} \Rightarrow \frac{ΔT}{T} = 2 \frac{Δn}{n}$
$\Rightarrow$ percentage change in Tension = $2 (1 %) = 2 %$

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