Question

Two sound sources $S_1$ and $S_2$ emit pure sinusoidal waves in phase. If the speed of sound is $330\text{m/s}$, then for what frequencies does constructive interference occur at P?

• A. $500\text{Hz}$
• B. $1000\text{Hz}$
• C. $1200\text{Hz}$
• D. $1500\text{Hz}$

Answer 1

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

The correct options are
A $500\text{Hz}$
B $1000\text{Hz}$
D $1500\text{Hz}$

Let ${}^{\prime }{O}^{\prime }$ be the midpoint between $S_1$ and $S_2$.
Seperation between two sound sources $S_1{S}_2=4.68\text{m}$
Path difference, $\Delta x=|S_{1}P-S_{2}P|$
From the data given in the question,

$\Delta x=(\sqrt{3^2+4^2}-\sqrt{4^2+{1.68}^2})=5-4.338\approx 0.66\text{m}$
Condition for constructive interference to occur,
$\Delta x=n\lambda =n\left(\frac{v}{f}\right)$ [where $n=1,2,3,....$]

$\Rightarrow f=\frac{nv}{\Delta x}=\frac{n\times 330}{0.66}\Rightarrow f=500n\text{Hz}$

For $n=1,f=500\text{Hz}$
For $n=2,f=1000\text{Hz}$
For $n=3,f=1500\text{Hz}$
and so on.
Thus, options (a), (b) and (d) are correct answers.