A lab technician wishes to determine the distance from ground to water level in a well by using an adjustable frequency oscillator in the audio range. Her assistant reports that she is able to establish two successive resonances at 51.76 Hz and 58.71 Hz. (Assume that the speed of sound in air is 343 m/s.) (a) How deep (in m) is the well? 28.169 The well acts like a pipe closed at one end. Write an expression for the length of the air column in terms of the number of quarter wavelengths for each case. How many more quarter wavelengths exist for the higher frequency case? See if you can quarter wavelengths for both frequencies and then the distance of interest. use this information to determine the number (b) How many antinodes are in the standing wave at 51.76 Hz? 17 In Part (a), you determined the number of quarter wavelengths associated with this frequency. Think of the number of quarter wavelengths as some number of whole wavelengths plus some additional quarter wavelengths. How many antinodes are associated with each whole wavelength? How many antinodes are associated with a quarter wavelength and with three quarter wavelengths? antinodes
A lab technician wishes to determine the distance from ground to water level in a well by using an adjustable frequency oscillator in the audio range. Her assistant reports that she is able to establish two successive resonances at 51.76 Hz and 58.71 Hz. (Assume that the speed of sound in air is 343 m/s.) (a) How deep (in m) is the well? 28.169 The well acts like a pipe closed at one end. Write an expression for the length of the air column in terms of the number of quarter wavelengths for each case. How many more quarter wavelengths exist for the higher frequency case? See if you can quarter wavelengths for both frequencies and then the distance of interest. use this information to determine the number (b) How many antinodes are in the standing wave at 51.76 Hz? 17 In Part (a), you determined the number of quarter wavelengths associated with this frequency. Think of the number of quarter wavelengths as some number of whole wavelengths plus some additional quarter wavelengths. How many antinodes are associated with each whole wavelength? How many antinodes are associated with a quarter wavelength and with three quarter wavelengths? antinodes
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Transcribed Image Text:A lab technician wishes to determine the distance from ground to water level in a well by using an adjustable frequency oscillator
in the audio range. Her assistant reports that she is able to establish two successive resonances at 51.76 Hz and 58.71 Hz.
(Assume that the speed of sound in air is 343 m/s.)
(a) How deep (in m) is the well?
28.169
The well acts like a pipe closed at one end. Write an expression for the length of the air column in terms of the number of
quarter wavelengths for each case. How many more quarter wavelengths exist for the higher frequency case? See if you can
use this information to determine the number of quarter wavelengths for both frequencies and then the distance of interest.
(b) How many antinodes are in the standing wave at 51.76 Hz?
17
In Part (a), you determined the number of quarter wavelengths associated with this frequency. Think of the number of
quarter wavelengths as some number of whole wavelengths plus some additional quarter wavelengths. How many antinodes
are associated with each whole wavelength? How many antinodes are associated with a quarter wavelength and with three
quarter wavelengths? antinodes
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