First slide

Beats

Question

Frequency of transverse oscillations of a taut string fixed at both ends is same as that of a tuning fork and when they oscillate together, beats of frequency 5 Hz are produced. If the tension in the string is slightly decreased the beat frequency is increased to 8 Hz. If frequency of the tuning fork is 450 Hz, what is the original frequency of the string?

Moderate

A

400 Hz
B

442 Hz
C

452 Hz
D

642 Hz

Solution

Frequency of transverse oscillations $f \propto \sqrt{T}$
Therefore if f be the original frequency of the string, we can write $450 - f = 8 \Rightarrow f = 442 H z$

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