Audible wavelengths. The range of audible frequencies is from about 20.0 Hz to 2

Question

Audible wavelengths. The range of audible frequencies is from about 20.0 Hz to 2.00 times 10^4 Hz What is range of the wavelengths of audible sound in air? Part B Visible light. The range of visible light extends from 400 nm to 700 nm. What is the range of visible frequencies of light? Part C Brain surgery. Surgeons can remove brain tumors by using a cavitron ultrasonic surgical aspirator which produces sound waves of frequency 23.0 kHz. What is the wavelength of these waves in air? Part 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?

Explanation / Answer

A) Wavelength = c / f, assuming speed of sound at 20°C: c = 343 m/s.

For the frequency f = 20 Hz the wavelength = c / f = 343 / 20 = 17.15 m.

For the frequency f = 20000 Hz the wavelength = c / f = 343 / 20000 = 0.01715 m = 1.715 cm.

B) Wavelength of visible light = 4×10^7 m to 7×10^7 m.

Speed of light c = 299792458 m/s.
For the wavelength = 400 nanometer the frequency f = c / = 299792458/4×10^7 = 7.495×10^14 Hz.
For the wavelength = 700 nanometer the frequency f = c / = 299792458 / 7×10^7 = 4.283×10^14 Hz.

C) Frequency f = 23 kHz = 23000 Hz at 20°C the wavelength = c / f = 343 / 23000 = 0.0149 m = 1.49 cm.

D) Frequency f = 23000 Hz. Speed of sound in water is c = 1480 m/s.
Wavelength = c / f = 1480 / 23000 = 0.06435 m = 6.435 cm.

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