A sound wave of amplitude 0.2mm has an intensity of 3W/m(squared). what will be the intensity of sound of same frequency having amplitude 0.4mm?

Seettiffrourfk6
2022-10-20
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Alannah Yang

Answered 2022-10-21
Author has **22** answers

Intensity is directly proportional to the square of the amplitude, i.e.

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

or

\frac{I_{1}}{I_{2}}=\frac{A_{1}^{2}}{A_{2}^{2}}\frac{I_{1}}{I_{2}}=\frac{A_{1}^{2}}{A_{2}^{2}}Show External URL Show Embeded Code Hide MathML CodeI1I2=A21A22$\frac{{I}_{1}}{{I}_{2}}=\frac{{A}_{1}^{2}}{{A}_{2}^{2}}$

where:

I is the intensity of the wave

A is the amplitude of the wave

So, we get:

$\frac{3W/{m}^{2}}{{I}_{2}}=\frac{(0.2mm{)}^{2}}{(0.4mm{)}^{2}}$

$=\frac{0.04m{m}^{2}}{0.16m{m}^{2}}$

$=\frac{1}{4}$

$\therefore {I}_{2}=\frac{4}{1}\ast 3W/{m}^{2}$

$=12W/{m}^{2}$

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

or

\frac{I_{1}}{I_{2}}=\frac{A_{1}^{2}}{A_{2}^{2}}\frac{I_{1}}{I_{2}}=\frac{A_{1}^{2}}{A_{2}^{2}}Show External URL Show Embeded Code Hide MathML CodeI1I2=A21A22$\frac{{I}_{1}}{{I}_{2}}=\frac{{A}_{1}^{2}}{{A}_{2}^{2}}$

where:

I is the intensity of the wave

A is the amplitude of the wave

So, we get:

$\frac{3W/{m}^{2}}{{I}_{2}}=\frac{(0.2mm{)}^{2}}{(0.4mm{)}^{2}}$

$=\frac{0.04m{m}^{2}}{0.16m{m}^{2}}$

$=\frac{1}{4}$

$\therefore {I}_{2}=\frac{4}{1}\ast 3W/{m}^{2}$

$=12W/{m}^{2}$

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