# Homework Help: Standing Waves on a string & pipe

1. Dec 18, 2012

### murrskeez

1. The problem statement, all variables and given/known data

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?

2. Relevant equations

Fn=(nV)/(2L)
λn=(2L)/n
V=√(F/μ) where μ=m/L

3. 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
Vstring=√(425N/0.0213kg/m) = 141.3m/s

2. Dec 18, 2012

### Staff: Mentor

What's the frequency of the vibrating string?

3. Dec 18, 2012

### murrskeez

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

so fn=(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.

4. Dec 18, 2012

### Staff: Mentor

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

5. Dec 18, 2012

### murrskeez

I think I get it

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

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

thank you so much, really appreciate it :)

6. Dec 18, 2012

Good!