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

In summary, the two problems are that you need to use f=nv/4L to find the speed of sound in a gas column of variable length, and that you need to calculate the maximum and minimum path difference for the different points on the circle the phase changes.
  • #1
loto
17
0
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.
 
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  • #2
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?
 
  • #3
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.
 
  • #4
Thanks guys, managed to get it figured out.
 

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

What is a 1024Hz tuning fork and how is it used?

A 1024Hz tuning fork is a small, metal instrument that produces a specific frequency of 1024Hz when struck. It is commonly used in scientific experiments and medical settings as a standard reference for measuring sound and vibration.

What are some common problems that can occur with a 1024Hz tuning fork?

Some common problems with a 1024Hz tuning fork include rust or corrosion, which can affect its ability to produce a consistent frequency. The tines of the fork can also become bent or damaged, which can alter the frequency it produces. Additionally, if the fork is not properly struck or held, it may not produce a clear sound.

How can I maintain my 1024Hz tuning fork to prevent problems?

To maintain your 1024Hz tuning fork, it is important to store it in a dry, cool place to prevent rust or corrosion. It should also be stored in a protective case or wrapped in a soft cloth to prevent damage to the tines. If the fork becomes dirty, it can be cleaned with a soft cloth and gentle soap or rubbing alcohol. Avoid using harsh chemicals or abrasive materials.

Why is it important to calibrate a 1024Hz tuning fork?

Calibrating a 1024Hz tuning fork ensures that it is producing the correct frequency and can be used as a reliable reference in scientific experiments or medical procedures. Over time, tuning forks can become slightly out of tune, so it is important to regularly calibrate them to maintain accuracy.

Can a 1024Hz tuning fork be used for other purposes besides measuring sound and vibration?

Yes, a 1024Hz tuning fork can also be used for other purposes, such as in music therapy or meditation. The consistent and soothing sound produced by the tuning fork can be used to promote relaxation and reduce stress. It can also be used in physics experiments or demonstrations to illustrate the properties of sound waves.

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