What is the amplitude of a gas element, at 20°C, when a sound wave of frequency 4 kHz propagates, and the pressure variation is 28 ìP, at the threshold of human hearing? A)2.7 × 10^-12 m B)1.7 × 10^-11 m C)1.7 × 10^-9 m D)2.7 × 10^-3 m

Question

Quizplus · Accepted Answer

The amplitude of a gas element when a sound wave propagates can be calculated using the formula for the pressure variation in a sound wave, which is $\Delta P = \rho v \omega A$, where $\Delta P$ is the pressure variation, $\rho$ is the density of the medium, $v$ is the speed of sound in the medium, $\omega$ is the angular frequency ($2\pi f$, with $f$ being the frequency), and $A$ is the amplitude. Given the pressure variation and the frequency, and knowing the speed of sound in air at 20°C is approximately 343 m/s and the density of air at this temperature is approximately 1.2 kg/m³, we can rearrange the formula to solve for $A$. The given pressure variation is very small (28 μPa, at the threshold of human hearing), indicating that the amplitude will also be very small, which aligns with option A, $2.7 \times 10^{-12}$ m, as the correct magnitude for such a scenario.

What Is the Amplitude of a Gas Element, at 20°C