A sound wave in brass has a displacement amplitude of $3.00 \mathrm{~mm}$. The frequency of the sound wave $750 \mathrm{~Hz}$ and the speed is $2,813 \mathrm{~m} / \mathrm{s}$. If the density of brass is $8.47 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$, then what is the pressure amplitude of the sound wave?
A) $3.37 \times 10^{8} \mathrm{~N} / \mathrm{m}^{2}$
B) $4.70 \times 10^{8} \mathrm{~N} / \mathrm{m}^{2}$
C) $4.17 \times 10^{8} \mathrm{~N} / \mathrm{m}^{2}$
D) $5.38 \times 10^{8} \mathrm{~N} / \mathrm{m}^{2}$
E) $5.10 \times 10^{8} \mathrm{~N} / \mathrm{m}^{2}$

Question

Quizplus · Accepted Answer

The pressure amplitude of a sound wave is given by:$$P_a = \rho v \omega A$$where:* $P_a$ is the pressure amplitude* $\rho$ is the density of the medium* $v$ is the speed of the sound wave* $\omega$ is the angular frequency* $A$ is the displacement amplitudePlugging in the given values, we get:$$P_a = (8.47 \times 10^3 \mathrm{~kg} / \mathrm{m}^3)(2,813 \mathrm{~m} / \mathrm{s})(2\pi 750 \mathrm{~Hz})(3.00 \times 10^{-3} \mathrm{~m})$$$$P_a = 3.37 \times 10^8 \mathrm{~N} / \mathrm{m}^2$$Therefore, the correct answer is A.

A Sound Wave in Brass Has a Displacement Amplitude Of 3.00