How Do Wavelengths Determine Sound Speed in a Closed Pipe?

AI Thread Summary
In a closed pipe of length 0.850m, a tuning fork at 512 Hz generates standing waves, with the open end acting as an antinode. The possible wavelengths calculated include 3.40 m, 1.13 m, 0.680 m, and 0.486 m, each corresponding to different speeds of sound in air. The most reasonable wavelength for calculating sound speed is 0.680 m, which aligns with the formula for wavelengths in closed pipes, Wavelength = 4L/(2n-1). Understanding standing waves and their harmonics is crucial for deriving these wavelengths. Mastery of this concept will aid in solving similar problems effectively.
dulaville
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Homework Statement

A tuning fork of frequency 512 Hz is used to generate a standing wave pattern in a closed pipe, 0.850m long. A strong resonant note is heard indicating that an antinode is located
at the open end of the pipe.

frequency = 512Hz
length = 0.850m

a - What are the possible wavelengths for this note?
b - Which wavelength will give the most reasonable value for the calculation of the speed of sound in air?

Now this is for HW and i have the answer, but all I need is to know how to figure out how to get there. Ideas?

a - 3.40 m @ 1.74 x 10^3 m/s
1.13 m @ 580 m/s
0.680 m @ 348 m/s
0.486 m @ 249 m/s
b - 0.680m

Thanks.
 
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You will need to know about standing waves and possible wavelengths to produce standing waves.
Have you been taught the derivation of the formula Wavelength = 4L/(2n-1) where n is the nth harmonic?
(Usually this is Taught as 4L/n where n = 1, 3, 5.. etc.
 
Look up some pictures from a textbook. That will help you understand where that equation comes from.
 

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