First slide

Standing waves

Question

Two identical wires are stretched by the same tension of 101 N and each emits a note of frequency 202 Hz. If the tension in one wire is increased by 1 N, then the beat frequency is:

Moderate

A

2 Hz
B

$\frac{1}{2} Hz$
C

1 Hz
D

none of these

Solution

$f \propto \sqrt{T}$
$f = \frac{1}{2 l} \sqrt{\frac{T}{μ}} \Rightarrow \frac{∆ f}{f} = \frac{1}{2} \frac{∆ T}{T}$
$\Rightarrow ∆ f = \frac{202}{2} \times \frac{1}{101} = 1$

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