Question

Tuning fork for A has frequency 1% greater than that of standard fork B while tuning fork C has frequency 2% smaller than that of B. When A and B are sounded together, then number of beats heard per second is 5. The frequency of tuning fork C is approximately

• A. $93Hz$
• B. $163Hz$
• C. $233Hz$
• D. $283Hz$

Answer 1

Answer: (B)

$163Hz$

If we consider the frequencies of the tuning forks A,B and C as $n_1,n_2$ and $n_3$.
This means the frequency of $n_1=n_2(1+.01)=1.01n_2$
$n_3=n_2\left(10.02\right)=0.98n_2$
But, $n_1{n}_3=5$ and $\left(1.01n_{2}0.98n_2\right)=5$
$n_2=166.7Hz$ (approx)
$n_3=0.98\times 166.7$
$n_3=163Hz$