A loudspeaker emits a sound wave of frequency 1.5 kHz1.5\text{ kHz}1.5 kHz into a room containing air at a temperature of 27∘C27^\circ\text{C}27∘C. The molar mass of air is 2.9×10−2 kg mol−12.9 \times 10^{-2}\text{ kg mol}^{-1}2.9×10−2 kg mol−1.
The maximum displacement of the air particles from their equilibrium positions due to the sound wave is 2.4×10−6 m2.4 \times 10^{-6}\text{ m}2.4×10−6 m.
Calculate:
The maximum speed vmaxv_{\text{max}}vmax of the oscillating air particles in the sound wave.
The root mean square speed cr.m.s.c_{\text{r.m.s.}}cr.m.s. of the air molecules in the room (where the molar gas constant is R=8.31 J mol−1 K−1R = 8.31\text{ J mol}^{-1}\text{ K}^{-1}R=8.31 J mol−1 K−1).