First slide

Travelling wave

Question

For a person with normal hearing the faintest sound that can be heard at a frequency of 400Hz has a pressure amplitude of about $6 \times 10^{- 5} {N/m}^{2}$ . Calculate the corresponding intensity in $W / m^{2}$ . Take speed of sound in air as 344m/s and density of air $1.2 kg / m^{3}$

Moderate

A

$4.4 \times 10^{- 3} W / m^{2}$
B

$4.4 \times 10^{- 12} W / m^{2}$
C

$4.4 \times 10^{- 4} W / m^{2}$
D

$4.4 \times 10^{- 1} W / m^{2}$

Solution

Given
Frequency $f = 400 Hz$
Pressure $Δ P = 6.0 \times 10^{- 5} pa$
Speed of sound in air $V = 344 m / s$
Density of air $ρ = 1.2 kg / m^{3}$
Intensity $I = \frac{v {(Δ P)}^{2}_{\max}}{2 B}$
Substituting $B = ρ v^{2}$ the above equation reduces to $I = \frac{(Δ P)_{max}^{2}}{2 ρ v}$
$\begin{matrix} = \frac{{(6.0 \times 10^{- 5})}^{2}}{2 \times 1.2 \times 344} = 0.0436 \times 10^{- 10} \\ ≃ 4.4 \times 10^{- 12} W / m^{2} \end{matrix}$

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