First slide

Beats

Question

Two identical stringed instruments have frequency 100 Hz. If tension in one of them is increased by 4% and they are sounded together then the number of beats in one second is

Difficult

A

1
B

8
C

4
D

2

Solution

Frequency of vibration in tight string
$n = \frac{p}{2 l} \sqrt{\frac{T}{m}} \Rightarrow n \propto \sqrt{T} \Rightarrow \frac{Δn}{n} = \frac{ΔT}{2 T} = \frac{1}{2} \times (4 %) = 2 %$
$\Rightarrow$ Number of beats = $Δn = \frac{2}{100} \times n = \frac{2}{100} \times 100 = 2$

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