Question

There is a set of $4$ tuning forks, one with lowest frequency vibrating at $552$ Hz. By using any two forks at time, the beat frequencies heard are $1,2,3,5,7,8$. The possible frequencies of other three forks are.

• A. $553,554$ and $560$ Hz
• B. $553,555$ and $560$ Hz
• C. $553,556$ and $558$ Hz
• D. $551,554$ and $560$ Hz

Answer 1

The correct option is A $553,554$ and $560$ Hz

$f_1=$ lowest

$=552Hz$ Let $(f_1<f_2<f_3<f_4)$

Different type of beat frequencies that can be heard $={4C}_2=6$

i.e $=(1,2,3,5,7,8)$

max beat freq $=$ $f_{max}-f_{mm}=8$

$\Rightarrow f_4-f_1=8$

$\Rightarrow f_4-552=8$

$\Rightarrow f_4=560Hz$

Now, $f_4-f_2=7$

$560-f_2=7$

$\Rightarrow f_2=553Hz$

We have-

$f_2-f_1=1$,

$f_4-f_2=7$,

$f_4-f_1=7$,

$\Rightarrow f_4-f_3=5$

$\Rightarrow 560-f_3=5$

$\Rightarrow f_3=555$

I am getting answer $553Hz$, $555Hz$, $560Hz$

But given answer is-

$553,554$ and $560Hz$

But this answer is wrong.

If we consider two frequencies $554Hz$ and $560Hz$ then beat freq $=6Hz$

but $6Hz$ is not given in the list of beat frequencies in the question. So, the given answer is wrong.