Question

When a stretched wire and a tuning fork are sounded together, $5$ beats per second are produced, when length of wire is $95cm$ or $100cm$, frequency of the fork is

• A. $90Hz$
• B. $100Hz$
• C. $105Hz$
• D. $195Hz$

Answer 1

Answer: (D)

$195Hz$

Let the frequency of tuning fork be $m$.
Suppose $l_1=95cm$ has frequency $n_1$ and $l_2=100cm$ has frequency $n_2(<n_1)$
Now, $n_1-n=5.....\left(i\right)$
$n-n_2=5.....\left(ii\right)$
Adding, we get $n_1-n_2=10.....\left(iii\right)$
Also, $\frac{n_1}{n_2}=\frac{l_2}{l_1}=\frac{100}{95}$
$n_1=\frac{100}{95}{n}_2$
From eqn. (iii), $\frac{100}{95}{n}_2-n_2=10,n_2=190$
From eqn. (ii), $n=n_2+5=190+5=195Hz$.