Standing Waves on a string & pipe

[murrskeez]

Homework Statement

A string 40.0cm long of mass 8.50g is fixed at both ends and is under a tension of 425N. When the string is vibrating in its third overtone, you observe that it causes a nearby pipe, open at both ends, to resonate in its third harmonic. The speed of sound is 344m/s. a) How long is the pipe? b) What is the fundamental frequency of the pipe?

Homework Equations

F_n=(nV)/(2L)
λ_n=(2L)/n
V=√(F/μ) where μ=m/L

The Attempt at a Solution

Really stuck on this one. I know I can find the velocity of the string with the given information but am not sure how I can relate the velocity of the string to the velocity of the pipe. Any suggestions would be much appreciated.

m/L= 0.0085kg/0.400m = 0.0213kg/m
V_string=√(425N/0.0213kg/m) = 141.3m/s

 

[Doc Al]

What's the frequency of the vibrating string?

 

[murrskeez]

So the third overtone would mean n=4...

so f_n=(4*141.3m/s)/(2*0.400m) = 706.5Hz

so the frequencies of the string and pipe must be related, I'm just not sure how.

 

[Doc Al]

So the third overtone would mean n=4...

so f_n=(4*141.3m/s)/(2*0.400m) = 706.5Hz

Good.

so the frequencies of the string and pipe must be related, I'm just not sure how.

They are the same! (They resonate.) So what's the fundamental frequency of the pipe?

 

[murrskeez]

I think I get it

f_pipe = nV/2L
706.5Hz = (3*344m/s)/(2L)
L = 0.730m

f_o = v/2L
f_o = (344m/s)/(2*0.730m)
f_o = 236Hz

thank you so much, really appreciate it :)

 

[Doc Al]

Good!