Question

$S_{1}and{S}_2$ are two coherent sources of sound having no initial phase difference. The velocity of sound is 330 m/s. No maxima 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. 330 Hz
• B. 120 Hz
• C. 100 Hz
• D. 220 Hz

Answer 1

The correct option is C 100 Hz

Let us consider a point at a distance $x$ from $S_2$ along the line passing through $S_2$. The path difference between sound from the two sources at that point=$\sqrt{3^2-x^2}-x$.

Thus the maximum path difference between them can be $3m$ for $x=0$. For maxima to be obtained, this path difference must be a multiple of wavelength.

Thus ${\lambda }_{max}=3m$

$c=\lambda \nu$

$⟹{\nu }_{min}=\frac{c}{{\lambda }_{max}}=110Hz$

Thus $\nu <110Hz$ if no maxima is obtained.