Answer to Question #172750 in Physics for Jerick

Question

  (a) Calculate the wavelengths in air at 20°C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. (b) What is the wavelength of an 18-MHz ultrasonic wave?

Answer 1

(a) The speed of sound at 20°C equals $343\ m/s$. Then, we can find the wavelengths from the wave speed formula:

$$v=f\lambda,$$ $$\lambda_{20\ Hz}=\dfrac{v}{f}=\dfrac{343\ \dfrac{m}{s}}{20\ Hz}=17.15\ m,$$ $$\lambda_{20\ kHz}=\dfrac{v}{f}=\dfrac{343\ \dfrac{m}{s}}{20\cdot10^3\ Hz}=1.7\cdot10^{-2}\ m$$

(b)

$$\lambda=\dfrac{v}{f}=\dfrac{343\ \dfrac{m}{s}}{18\cdot10^{6}\ Hz}=1.9\cdot10^{-5}\ m.$$