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Giancoli's Physics: Principles with Applications, 7th Edition
12
Sound
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12-1: Characteristics of Sound
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12-2: Intensity of Sound; Decibels
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12-3: Loudness
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12-4: Sources of Sound: Strings and Air Columns
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12-5: Quality of Sound, Superposition
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12-6: Interference; Beats
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12-7: Doppler Effect
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12-8: Shock Waves; Sonic Booms
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Question by Giancoli, Douglas C., Physics: Principles with Applications, 7th Ed., ©2014, Reprinted by permission of Pearson Education Inc., New York.
Problem 3
Q
  1. Calculate the wavelengths in air at 20∘C20 ^\circ \textrm{C} for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz.
  2. What is the wavelength of an 18-MHz ultrasonic wave?
A
  1. λ20 Hz=17 m, λ20 kHz=1.7 cm\lambda_{20\textrm{ Hz}} = 17 \textrm{ m, } \lambda_{20 \textrm{ kHz}} = 1.7 \textrm{ cm}
  2. 1.9×10−5 m1.9 \times 10^{-5} \textrm{ m}
Giancoli 7th Edition, Chapter 12, Problem 3 solution video poster
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VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. Wave speed is frequency times wavelength when we divide both sides by f we can solve for λ the wavelength is the speed of sound divided by its frequency. So, the wavelength at 20 hertz is 343 meters per second speed of sound, divided by 20 hertz which is about 17 meters. And then at 20,000 hertz or 20 kilohertz the wavelengths will be 343 meters per second divided by 20,000 which is about 1.7 centimeters when you convert those then, you know, it's 0.017 meters but 1.7 centimeters is easier to think about. And then in part b the wavelength for an 18 mega hertz sound would be 343 meters per second divided by 18 times 10 to the 6, because that's the exponent for 10 when you have the prefix in mega 10 to the 6 and then you have 1.9 times 10 to the minus 5 meters.

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