First slide

Standing waves

Question

Two identical piano wires kept under the same tension have a fundamental frequency of 600 Hz. The fractional increase in the tension of one of the wires which will lead to occurrence of 6 beat/s when both the wires oscillate together would be

Moderate

A

0.02
B

0.03
C

0.04
D

0.01

Solution

According to law of tension, the frequency of the string varies directly as the square root of its tension
$n \propto \sqrt{T}$
$\frac{∆ n}{n} = \frac{1}{2} . \frac{∆ T}{T}$
or $\frac{∆ T}{T} = 2 \times \frac{∆ n}{n}$
$\frac{∆ T}{T} = 2 \times \frac{6}{600} = 0.02$

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