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Solved: (a) Audible wavelengths. The range of audible
Chapter 15, Problem 5E(choose chapter or problem)
Problem 5E
(a) Audible wavelengths. The range of audible frequencies is from about 20 Hz to 20,000 Hz. What is the range of the wavelengths of audible sound in air? (b) Visible light. The range of visible light extends from 400 nm to 700 nm. What is the range of visible frequencies of light? (c) Brain surgery. Surgeons can remove brain tumors by using a cavitron ultrasonic surgical aspirator, which produces sound waves of frequency 23 kHz. What is the wavelength of these waves in air? (d) Sound in the body. What would be the wavelength of the sound in part (c) in bodily fluids in which the speed of sound is 1480 m/s but the frequency is unchanged?
Questions & Answers
QUESTION:
Problem 5E
(a) Audible wavelengths. The range of audible frequencies is from about 20 Hz to 20,000 Hz. What is the range of the wavelengths of audible sound in air? (b) Visible light. The range of visible light extends from 400 nm to 700 nm. What is the range of visible frequencies of light? (c) Brain surgery. Surgeons can remove brain tumors by using a cavitron ultrasonic surgical aspirator, which produces sound waves of frequency 23 kHz. What is the wavelength of these waves in air? (d) Sound in the body. What would be the wavelength of the sound in part (c) in bodily fluids in which the speed of sound is 1480 m/s but the frequency is unchanged?
ANSWER:Solution 5E
Step 1:
a) Suppose, the speed of sound in air at 20℃ is, v = 343 m/s
Equation for the speed of sound, v = f𝜆
Where, f - frequency of the wave
𝜆 - Wavelength of the wave
Minimum frequency in audible range, fmin = 20 Hz
Rearranging the equation, 𝜆 = v/f
Wavelength of the wave at minimum frequency, 𝜆min = v/fmin
𝜆min = 343m/s / 20 Hz
𝜆min = 17.15 m
Maximum frequency in audible range, fmax = 20,000 Hz
𝜆max = v/fmax
𝜆max = 343 m/s / 20,000 Hz = 0.0172 m
Range of audible wavelength, 0.0172 m to 17.15 m