Formula to find velocity of sound using resonance tube
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Object: To observe the resonance phenomenon in an open ended cylindrical tube. To use the resonance to determine the velocity of sound in air at ordinary temperatures.
Introduction: The velocity with which sound travels in any medium may be determined if the frequency and the wavelength are known. The relationship between these quantities is:
v = fλ wherev = velocity of sound propagation
f = frequency
λ = wavelength
In this experiment the velocity of sound in air is to be found by using tuning forks of known frequency. The wavelength of the sound will be determined by making use of the resonance of an air column.
The apparatus for the experiment consists of a long cylindrical plastic tube attached to a water reservoir. The length of the water column may be changed by raising or lowering the water level while the tuning fork is held over the open end of the tube. Resonance is indicated by the sudden increase in the intensity of the sound when the column is adjusted to the proper length. The resonance is a standing wave phenomenon in the air column and occurs when the column length is:
λ/4, 3λ/4, 5λ /4
where λ is the sound wavelength.
The water surface constitutes a node of the standing wave since the air is not free to move longitudinally. The open end provides the conditions for an antinode, but the actual antinode has been found to occur outside the tube at a distance of about 0.6 r from the end, where r is the tube radius. This end correction may be added to get a more accurate value if only one resonance can be measured, but it is usually more convenient to eliminate this "end effect" by subtracting the resonance length for λ/4 from those for 3 λ /4, 5λ /4, etc.

Introduction: The velocity with which sound travels in any medium may be determined if the frequency and the wavelength are known. The relationship between these quantities is:
v = fλ wherev = velocity of sound propagation
f = frequency
λ = wavelength
In this experiment the velocity of sound in air is to be found by using tuning forks of known frequency. The wavelength of the sound will be determined by making use of the resonance of an air column.
The apparatus for the experiment consists of a long cylindrical plastic tube attached to a water reservoir. The length of the water column may be changed by raising or lowering the water level while the tuning fork is held over the open end of the tube. Resonance is indicated by the sudden increase in the intensity of the sound when the column is adjusted to the proper length. The resonance is a standing wave phenomenon in the air column and occurs when the column length is:
λ/4, 3λ/4, 5λ /4
where λ is the sound wavelength.
The water surface constitutes a node of the standing wave since the air is not free to move longitudinally. The open end provides the conditions for an antinode, but the actual antinode has been found to occur outside the tube at a distance of about 0.6 r from the end, where r is the tube radius. This end correction may be added to get a more accurate value if only one resonance can be measured, but it is usually more convenient to eliminate this "end effect" by subtracting the resonance length for λ/4 from those for 3 λ /4, 5λ /4, etc.

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