# 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?

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?
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Alannah Yang
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:
$\frac{3W/{m}^{2}}{{I}_{2}}=\frac{\left(0.2mm{\right)}^{2}}{\left(0.4mm{\right)}^{2}}$
$=\frac{0.04m{m}^{2}}{0.16m{m}^{2}}$
$=\frac{1}{4}$
$\therefore {I}_{2}=\frac{4}{1}\ast 3W/{m}^{2}$
$=12W/{m}^{2}$