How Do Wavelengths Determine Sound Speed in a Closed Pipe?

[dulaville]

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.

 

[inutard]

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.

 

[cartonn30gel]

Look up some pictures from a textbook. That will help you understand where that equation comes from.