Question

Two tuning forks $X$ and $Y$ are of frequencies $280Hz$ and $284Hz$. A third tuning fork $Z$ is of unknown frequency, when $X$ and $Z$ are sounded together certain beats are heard per second. When $Y$ and $Z$ are sounded together beat frequency is found to be thrice as great. The frequency of $Z$ is

• A. $282Hz$
• B. $286Hz$
• C. $280Hz$
• D. $278Hz$

Answer 1

Answer: (D)

Given, frequency of tuning fork $X$ and $Y$ are,
$n_X=280Hz$
$n_Y=284Hz$
$n_Z=?$
When tuning forks $X$ and $Z$ are sounded together, then beats produced is $b$ (assume).
$\therefore n_z-n_X=b...$ (i)
Again, when $Y$ and $Z$ are sounded together, then
$n_z-n_Y=3b...$ (ii)
Dividing Eq. (i) by Eq. (ii), we have
$\frac{n_Z-n_X}{n_Z-n_Y}=\frac{b}{3b}$
$\Rightarrow \frac{n_Z-280}{n_Z-284}=\frac{1}{3}$
$\Rightarrow 3n_z-840=n_z-284$
$\Rightarrow 3n_z-n_Z=840-284$
$\Rightarrow 2n_Z=556$
$\Rightarrow n_Z=278Hz$