Asst 25 Interference

course Phy 202

????|??x??Z???assignment #024024. `Query 13

Your work has been received. Please scroll through the document to see any inserted notes (inserted at the appropriate place in the document, in boldface) and a note at the end. The note at the end of the file will confirm that the file has been reviewed; be sure to read that note. If there is no note at the end, notify the instructor through the Submit Work form, and include the date of the posting to your access page.

Physics II

09-02-2007

???D????y????

assignment #025

025. `Query 14

Physics II

09-02-2007

......!!!!!!!!...................................

19:43:09

Query Principles of Physics and General College Physics 12.40: Beat frequency at 262 and 277 Hz; beat frequency two octaves lower.

......!!!!!!!!...................................

RESPONSE -->

The beat f is the difference between the frequencies.

277 - 262 = 15 beats /sec

If both frequencies are reduced by a factor of four, the beat f will be:

(277 /4) - (262 / 4) = 3.75 beats / sec.

.................................................

......!!!!!!!!...................................

19:43:16

The beat frequency is the difference in the frequencies, in this case 277 Hz - 262 Hz = 15 Hz.

One ocatave reduces frequency by half, so two octaves lower would give frequencies 1/4 as great. The difference in the frequencies would therefore also be 1/4 as great, resulting in a beat frequency of 1/4 * 15 Hz = 3.75 Hz.

......!!!!!!!!...................................

RESPONSE -->

ok

.................................................

......!!!!!!!!...................................

19:54:38

Query gen phy problem 12.46 speakers 1.8 meters apart, listener three meters from one and 3.5 m from the other **** gen phy what is the lowest frequency that will permit destructive interference at the location of the listener?

......!!!!!!!!...................................

RESPONSE -->

Person must be 1/2 wavelength closer to one speaker than the other. The difference the person is standing between the two speakers is 3.5 m - 3 m = .5 m. So .5 *2 = 1 m. So the wavelength is 1 m. f = vel / lambda = 343 m/s / 1 m = 343 Hz

.................................................

......!!!!!!!!...................................

20:13:01

STUDENT SOLUTION: To solve this problem, I first realize that for destructive interference to occur, the path difference is an odd multiple of half of the wavelength(ex. 1/2, 3/2, 5/2). I used Fig.12-17 in the text to help visualize this problem. Part (A) of the problem asks to calculate the lowest frequency at which destructive interference will occur at the point where two loudspeakers are 2.5m apart and one person stands 3.0m from one speaker and 3.5m from the other. The text states that 'destructive interference occurs at any point whose distance from one speaker is greater than its distance from the other speaker by exactly one-half wavelength.' The path difference in the problem is fixed, therefore the lowest frequency at which destructive interference will occur is directly related to the longest wavelength. To calculate the lowest frequency, I first have to calculate the longest wavelength using the equation

'dL ='lambda/2, where `dL is the path difference.

'lambda=2*'dL

=2(3.5m-3.0m)=1m

Now I can calculate the frequency using

f=v/'lambda. The velocity is 343m/s which is the speed of sound.

f=343m/s/1m=343 Hz.

Thus, the lowest frequency at which destructive interference can occur is at 343Hz.

Keeping in mind that destructive interference occurs if the distance equals an odd multiple of the wavelength, I can calculate (B) part of the problem.

To determine the next wavelength, I use the equation 'dL=3'lambda/2

wavelength=2/3(3.5m-3.0m) =0.33m

Now I calculate the next highest frequency using the equation f=v/wavelength.

f^2=343m/s/0.33m=1030Hz.

I finally calculate the next highest frequency.

'del L=5/2 'lambda

wavelength=0.20m

f^3=343m/s/0.2m=1715 Hz.

INSTRUCTOR EXPLANATION:

The listener is .5 meters further from one speaker than from the other. If this .5 meter difference results in a half-wavelength lag in the sound from the further speaker, the peaks from the first speaker will meet the troughs from the second. If a half-wavelength corresponds to .5 meters, then the wavelength must be 1 meter. The frequency of a sound with a 1-meter wavelength moving at 343 m/s will be 343 cycles/sec, or 343 Hz.

The next two wavelengths that would result in destructive interference would have 1.5 and 2.5 wavelengths corresponding to the .5 m path difference. The wavelengths would therefore be .5 m / (1.5) = .33 m and .5 m / (2.5) = .2 m, with corresponding frequencies 343 m/s / (.33 m) = 1030 Hz and 343 m/s / (.2 m) = 1720 Hz, approx. ****

......!!!!!!!!...................................

RESPONSE -->

I thought we only had to answer part a

.................................................

......!!!!!!!!...................................

20:16:11

**** gen phy why is there no highest frequency that will permit destructive interference?

......!!!!!!!!...................................

RESPONSE -->

No matter how high the frequencies, they can still intersect and cause distructive interference

.................................................

......!!!!!!!!...................................

20:16:28

** You can get any number of half-wavelengths into that .5 meter path difference. **

......!!!!!!!!...................................

RESPONSE -->

ok i get this

.................................................

......!!!!!!!!...................................

20:21:53

gen phy what must happen in order for the sounds from the two speakers to interfere destructively, assuming that the sources are in phase?

......!!!!!!!!...................................

RESPONSE -->

The highest amplitude of one wave and the lowest amplitude of the other wave must meet at a point so that they cancel each other out.

.................................................

......!!!!!!!!...................................

20:22:37

** The path difference has to be and integer number of wavelengths plus a half wavelength. **

......!!!!!!!!...................................

RESPONSE -->

ok, yes they must be half a wave length apart

.................................................

......!!!!!!!!...................................

20:25:27

CRAB NEBULA PROBLEM?

......!!!!!!!!...................................

RESPONSE -->

what are you reffering to?

that was just an extraneous note, which you can safely ignore

................................................."

This looks good. Let me know if you have questions.