Question

$S_1\text{and}{S}_2$ are two coherent sources of sound having same frequency (110 Hz) each. They are vibrating in phase. The intensity at $P$ due to $S_1\text{is}{I}_0$ and due to $S_2$ is $4I_0$. If the velocity of sound is $330\text{m/s}$ then resultant intensity at $P$ is $k{I}_0$. The value of $k$ is

• A. 3.0
• B. 3
• C. 3.00

Answer 1

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

$\Delta \varphi =\frac{2\pi }{\lambda }\times \Delta x$
and, $\Delta x=S_{2}P-S_{1}P=5-4=1$
Also, $v=f\lambda$
$\Rightarrow \lambda =\frac{330}{110}=3$
$\therefore \Delta \varphi =\frac{2\pi }{3}$
Now, we know that
$I_{net}=I_0+4I_0+2\sqrt{I_0\times 4I_0}\cos \frac{2\pi }{3}$
Hence, $I_{net}=3I_0$
So, $k=3$