Question

Two notes $A$ and $B$, sounded together, produce $2$ beats per second. Notes $B$ and $C$ sounded together produces $3$ beats per sec. The notes $A$ and $C$ separately produce the same number of beats with a standard tuning fork of $456\text{Hz}$. The possible frequency of the note $B$ is

• A. $453.5\text{Hz}$
• B. $455.5\text{Hz}$
• C. $456.5\text{Hz}$
• D. $458.5\text{Hz}$

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A $453.5\text{Hz}$
B $455.5\text{Hz}$
C $456.5\text{Hz}$
D $458.5\text{Hz}$

Let frequency of note $B$ be $n$ then according to question
$n_A=n-2$ or $n+2$
$n_C=n-3$ or $n+3$
As $A$ and $C$ produce same number of beats with Tuning fork of frequency $456Hz$ so
$(n-2)-456=456-(n-3)$
$\Rightarrow n=458.5\text{Hz}$
$(n+3)-456=456-(n-2)$
$\Rightarrow n=455.5\text{Hz}$
$(n+2)-456=456-(n-3)$
$\Rightarrow n=456.5\text{Hz}$
$(n+3)-456=456-(n+2)$
$\Rightarrow n=453.5\text{Hz}$