First slide

Beats

Question

A tuning fork of known frequency 256 Hz makes 5 beats per second with the vibrating string of a piano. The beat frequency decreases to 2 beats per second when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was

Moderate

A

256 + 5 Hz
B

256 + 2Hz
C

256 – 2 Hz
D

256 – 5Hz

Solution

Suppose n_P = frequency of piano = ? $(n_{P} \propto \sqrt{T})$
n_f = Frequency of tuning fork = 256 Hz
x = Beat frequency = 5 bps, which is decreasing (5 $\to$ 2) after clanging the tension of piano wire
Also, tension of piano wire is increasing so n_P $↓$
Hence n_P $↑$ – n_f = x $↓$ $\to$ Wrong
n_f – n_P $↑$ = x $↓$ $\to$ Correct
$\Rightarrow$ n_P = n_f – x = 256 – 5 Hz.

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