Question

The ratio of intensity of two sounds A and B is 9:16. If the amplitude of sound A is doubled and that of sound B is halved, then the ratio of sound becomes-​

Answer 1

Explanation:

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Answer 2

Answer:

The ratio of the sound becomes 9.

Explanation:

A sound wave exists in the pattern of a disturbance generated by the movement of energy traveling through a medium (such as air, water, or any other liquid or solid matter) as it propagates out from the source of the sound.

Sound waves I $\propto A^{2}$

$\frac{I_{1}}{I_{2}}=\left(\frac{A_{1}}{A_{2}}\right)^{2}$

$\Rightarrow\left(\frac{9}{16}\right)^{\frac{1}{2}}=\frac{A_{1}}{A_{2}}$

Simplifying the above equation, we get

$\frac{A_{1}}{A_{2}}=\frac{3}{4} \longrightarrow(1)$

$\quad A_{1}^{\prime}=2 A$

$A_{2}^{\prime}=\frac{A_{2}}{2}$

then,

$\frac{I_{1}^{\prime}}{I_{2}^{\prime}}= \left(\frac{A_{1}^{\prime}}{A_{2}^{\prime}}\right)^{2}$$=\left(4 \frac{A_{1}}{A_{2}}\right)^{2}$

$\frac{I_{1}^{\prime}}{I_{2}}=16 \times \frac{9}{16}=\frac{9}{1}$

Therefore, the ratio of the sound becomes 9.

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