# Homework Help: Using frequency to calculate resonances

1. Apr 10, 2010

### jimisreincarn

1. If the length of the tube used in our experiment is 4 m, how many resonances would you observe when a tuning fork of frequency 256HZ is used?

2. v=f$$\lambda$$ ; L = (1/4)(2n+1)$$\lambda$$

3. 340m/s = 256Hz$$\lambda$$ $$\lambda$$ = 1.328125m
4 = (1/4)(2n+1)(1.328125m)
12.05 = 2n+1
5.5 = n

2. Apr 10, 2010

### AtticusFinch

We need to know what kind of tube you used in lab (open, one end closed, etc.)

3. Apr 10, 2010

### jimisreincarn

one end of the tube is open. The other end has water at the end of it.

4. Apr 10, 2010

### AtticusFinch

Ok and you probably raised the water level while ringing the tuning fork and marked where you heard resonances, right?

So this is a closed end tube. You are correct in using the equation $$L = \frac{2n+1}{4}\lambda$$

However, you are not correct in leaving L at 4 because you raised and lowered the water level. What you should do is evaluate the inequality $$4 \leq \frac{2n+1}{4}\lambda$$
and solve for n. Of course you are only allowed integer values of n.

5. Apr 10, 2010

### jimisreincarn

okay, that makes sense. so if my evaluation of the wavelength is correct, i would substitute it into the inequality and I should get n < 5? so at most there are 5 resonance structures.

6. Apr 10, 2010

### AtticusFinch

Yep, that is what I get as well.