Question

$S_1$and $S_2$ are two coherent sources of sound having no initial phase difference. The velocity of sound is $330m/s$. No minima will be formed on the line passing through $S_2$ and perpendicular to the line joining $S_1$ and $S_2$, if the frequency of both the sources is:

• A. $60Hz$
• B. $50Hz$
• C. $70Hz$
• D. $80Hz$

Answer 1

The correct option is B $50Hz$

For minimum interference, an expression for path difference is,
$(2n-1)\frac{\lambda }{2}$

Here, the difference between the two sources is $3m$.
In this case for no minima,
$\frac{\lambda }{2}>3\text{or}\lambda >6.$

Consider wavelength approximately as
$\lambda \sim 6.$

Frequency can be expressed as,
$f=\frac{V}{\lambda }<\frac{330}{6}\text{or}f<55$

Hence, the frequency is less than $55$.

Final Answer: (a)