Resonance and Sound Waves: Calculating Speed of Sound and Phase Differences

[loto]

Hi all,

I'm working through a sample midterm and I managed to get everything correct except for two, which I am a bit stuck on. Here is the first one:

A 1024Hz tuning fork is used to obtain a series of resonance levels in a gas column of variable length, with one end closed and the other open. The length of the column changes by 20cm from resonance to resonance. From this data, the speed of sound in this gas is: (Answer: 410m/s)

I know I have to use f=nv/4L, and I know the answer is equal to v=f2L, but I'm not sure how to get to that point.

The second one:

Two isotropic sources of sound, S1 and S2, emit waves in phase at a wavelength of .50m. As shown in the figure, they are separated by distance D=1.75m. If we move a sound detector around a large circle with radius r>>D and centered at the midpoint between the sources, at how many points do waves arrive at the detector exactly in phase? You may wish to consider two "extreme" situations in the process of answering this question - on the large circle directly above the two sources, and on the large circle on a line directly to the right (or left) of the two sources. (Answer: 14 points)

Diagram: *S1 <------D-----> *S2

With this one, I'm assuming that: Phi=(Delta Length)2Pi / Lamda, where we finde the values of (Delta Length) that equal a set of positive integers, but I am unsure how to actually do this.

Any hints or tips would be much appreciated. Thanks.

 

[lightgrav]

You ARE drawing these wave forms in the tube ...?
They told you that ½ wavelength = 20 cm, and
gave you the frequency ... sounds like a job for "v"!

2nd problem is 2-source constructive interference.
path length difference must be "n lamda"
for constructive interference to occur;
2 parallel rays (one from each source) at theta
from centerline meet at screen out-of-step by
( \ \ )
( \ _ x | )
( V \ | )
d sin theta . What is n for -90 < theta < 90 deg?

 

[mukundpa]

1. Go through the standing waves in a closed organ pipe.

the formula is f = (2n + 1)v/4L

2. For the different points on the circle the phase changes, how?
Try to calculate maximum and minimum path difference, this will give you the idea.

 

[loto]

Thanks guys, managed to get it figured out.