An acoustic transducer in a sealed chamber filled with argon gas emits a sound wave of frequency 24 kHz24\text{ kHz}24 kHz. The chamber is maintained at a temperature of 127∘C127^\circ\text{C}127∘C. The molar mass of argon is 3.99×10−2 kg mol−13.99 \times 10^{-2}\text{ kg mol}^{-1}3.99×10−2 kg mol−1.
The maximum displacement of the argon atoms from their equilibrium positions due to the sound wave is 1.8×10−7 m1.8 \times 10^{-7}\text{ m}1.8×10−7 m.
Calculate:
The maximum speed vmaxv_{\text{max}}vmax of the oscillating argon atoms in the sound wave.
The root mean square speed cr.m.s.c_{\text{r.m.s.}}cr.m.s. of the argon atoms in the chamber (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).