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$S_1$ and $S_2$ are two coherent sources of sound of frequency $260 \mathrm{kz}$ . They have no initial phase difference. The intensity at a point p due to s_1 is 6 I_0 and due to $\mathrm{S}_2$ is $8I_0$ . If the velocity of sound is $340 \mathrm{~m} / \mathrm{s}$ then the resultant intensity at $P$ .
Option: 1
$15.25\,I_0$

Option: 2
$15.45\,I_0$

Option: 3
$15.15\,I_0$

Option: 4
$15.35\,I_0$

Answers (1)

best_answer

$\lambda=\frac{V}{n}=\frac{340}{260}=\frac{34}{26}=\frac{17}{13}$

$\varphi=$ Phase difference

$\varphi=\frac{2 \pi}{1} \times \Delta x$ $\varphi=\frac{2 \pi}{\lambda} \times \Delta x$

$\varphi=\frac{2 \pi}{\lambda}(13-12)$

$\varphi=\frac{2 \pi}{\lambda} \times 1 \\$

$\varphi=\frac{2 \pi}{\lambda}$

$I=I_1+I_2+2 \sqrt{I_1 . I_2} \cdot \operatorname{Cos\varphi } \\$

$I=6 I_0+8I_0+2 \sqrt{6I_0.8I_0} \cdot \operatorname{Cos} \frac{2 \pi}{\lambda} \\$

$I=14 I_0+2 \sqrt{48 I_0^2} \cdot Cos \frac{2 \pi}{\lambda} \\$

$I=14 I_0+2 I_0 \sqrt{48} \cdot\left(Cos \frac{2 \pi}{\frac{17}{13}}\right). \\$

$I=14 I_0+2 I_0 \times 4 \sqrt{3} \cdot \cos \frac{2 \times 13 \pi}{17} \\$

$I=14 I_0+8I_0 \sqrt{3} \cdot \operatorname{Cos} \frac{26 \pi}{17} \\$

$I=14 I_0+8 I_0 \times 1.732 \times 0.1046 \\$

$I=14 I_0+8 I_0 \times 0.1812 \\$

$I=14 I_0+1.45 I_0 \\$

$I=15.45I_0$

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