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Answer in Physics for Jerick #172750

Author:
January 25th, 2023

  (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?

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

“v=flambda,”“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}}{20cdot10^3 Hz}=1.7cdot10^{-2} m”

(b)

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

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