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

Question

a. Audible wavelengths.The range of audible frequencies is from about 20.0 Hz to 2.00×104 Hz. What is 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 23.0 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?

Explanation / Answer

a) The range of audible frequencies in the air is from about 20.0 Hz to 2.00×104 Hz The speed of the sound in air is 340 m/s The minimum wavelength min = v/fmax                                                         = (340 m/s)/(2*104 Hz)                                                         = 0.017 m                                                         The maximum wavelength max = v/fmin                                                         = (340 m/s)/(20 Hz)                                                         = 17 m                                                                                                                  = (340 m/s)/(2*104 Hz)                                                         = 0.017 m                                                                                                                 = (340 m/s)/(20 Hz)                                                         = 17 m                                                          The range of the wavelengths of audible sound in air is 0.017 m to 17 m b) The range of visible light extends from 400 nm to 700 nm speed of light c = 3*108 m/s The minimum frequency fmin = c/max                                                  = (3*108 m/s)/(700*10-9 m)                                                  = 4.28*1014 Hz The maximum frequency fmax = c/min                                                  = (3*108 m/s)/(400*10-9 m)                                                  = 7.5*1014 Hz the range of visible frequencies of light is 4.28*1014 Hz to 7.5*1014 Hz c) The frequency of the sound wave is f = 23 kHz the wavelength is = v/f                                  = (340 m/s)/(23*103 hZ)                                  = 0.015 m d) The speed of the sound in body fluid is v = 1480 m/s the wavelength is = v/f                                  = (1480 m/s)/(23*103 hZ)                                  = 0.064 m                                                  = (3*108 m/s)/(700*10-9 m)                                                  = 4.28*1014 Hz The maximum frequency fmax = c/min                                                  = (3*108 m/s)/(400*10-9 m)                                                  = 7.5*1014 Hz                                                  = (3*108 m/s)/(400*10-9 m)                                                  = 7.5*1014 Hz the range of visible frequencies of light is 4.28*1014 Hz to 7.5*1014 Hz c) The frequency of the sound wave is f = 23 kHz the wavelength is = v/f                                  = (340 m/s)/(23*103 hZ)                                  = 0.015 m d) The speed of the sound in body fluid is v = 1480 m/s the wavelength is = v/f                                  = (1480 m/s)/(23*103 hZ)                                  = 0.064 m the wavelength is = v/f                                  = (1480 m/s)/(23*103 hZ)                                  = 0.064 m

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