First slide

Beats

Question

The frequency of B is 3% greater than that of A. The frequency of C is 2% less than that of A. If B and C produce 8 beats/s, then the frequency of A is

Easy

A

136 Hz
B

168 Hz
C

164 Hz
D

160 Hz

Solution

$v_{B} = v_{A} + \frac{3}{100} v_{A}$
$v_{C} = v_{A} - \frac{2}{100} v_{A}$ $\Rightarrow$ $\frac{3}{100} v_{A} + \frac{2}{100} v_{A} = 8$ $\Rightarrow v_{A} \times \frac{5}{100} = 8$ or $v_{A}$ = 160 Hz

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