monster beat frequency question.

[SaintJude]

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Just when I though beat frequency was the most straight forward topic, Kaplan sends me this question..😱

At the end of the show, the audience is clapping enthusiastically. A physics student who is in the audience measures that the lower level is clapping with a frequency of 5 claps/second, while the first and second balconies clap with a frequency of 4 claps/second and 2 claps/second, respectively. What is the beat frequency at which the big round of applause of all three seating levels can be heard?

A. ) -1claps/second
B.) 1 claps/second
C. ) 0 claps/ second
D. 2 claps/second

Edit: No longer sure this question makes sense....Milksi says ignore...

 

[MedPR]

Just when I though beat frequency was the most straight forward topic, Kaplan sends me this question..😱

At the end of the show, the audience is clapping enthusiastically. A physics student who is in the audience measures that the lower level is clapping with a frequency of 5 claps/second, while the first and second balconies clap with a frequency of 4 claps/second and 2 claps/second, respectively. What is the beat frequency at which the big round of applause of all three seating levels can be heard?

A. ) -1claps/second
B.) 1 claps/second
C. ) 0 claps/ second
D. 2 claps/second

Edit: Nevermind! Answer is (highlight) : B
Gotta love Kaplan for pushing concepts & definitions.

I guessed B because I figured that every 2 seconds the first and second balcony clapping would overlap, so 5-4 = 1.

What is the explanation?

 

[milski]

While I know what they want me to answer, that's just wrong. Just because two events are repetitive and have frequencies does not mean that you can use formulas applicable only for simple harmonic motions. 😱🙄

I hope that the real MCAT has better questions writers.

 

[milski]

I guessed B because I figured that every 2 seconds the first and second balcony clapping would overlap, so 5-4 = 1.

What is the explanation?

That's their idea. It implies that the claps themselves are in phase (kind of possible) and harmonic (very hard to stomach).

But the other answers don't make sense with just about any assumptions which would make this the best one.

 

[SaintJude]

That's not the idea or explanation given. The explanation is actually quite simple, but now that you guys are discussing it, I wonder if it's valid...

Anyway the beat frequency, by definition, is the absolute value of the difference of closely related frequencies. So answer is |5-4-2| =1

 

[milski]

Just when I thought they could not screw up further. 👎

As it is, they don't make sense. Why |5-4-2| and not |2-5-4| or |4-5-2|? The combination of three frequencies will not necessary lead to a single beat frequency. I would just forget about the question.

If you wanted to know more about what happens when you have 3 freqs, you need to consider the differences between each two of them. From there, things get easier or more complicated, depending on wether the resulting numbers are multiples of each other or not. It certainly is not a single +/- formula as with the two frequencies case.

 

[SaintJude]

Yeah, milski, maybe you're right. In fact, you probably are.

 

[milski]

For what it's worth, here is the graph (with harmonic clapping):

 

[chiddler]

perhaps because they split it in to two levels, the floor and balcony.

floor is 5 hz, balcony is 4 and 2.

so you can either go 6-5 or 5-6. since it's absolute value it doesn't matter.

 

[SaintJude]

What the y-axis? frequency can't be negative (right?)

 

[milski]

What the y-axis? frequency can't be negative (right?)

In the graph? Intensity. It's the sum of three harmonics with frequencies of 2,4 and 5.

 

[SaintJude]

Damn, milski, who are you?! Please and take statement as the utmost form of flattery.

So what is this graph saying? PLEASE explain, because I'm very interested. Is this showing the beat frequencies?

 

[milski]

Ok, here comes a long post. 😉

The way to read the graph - the distance between the peaks of the graph corresponds to the frequency of the signal, so the closer they are to each other, the higher the frequency and the higher pitch you're going to hear.

The displacement along the y-axis corresponds to intensity or how loud you're going to hear the signal.

Based on that, you cannot say many nice things about the graph of 2/4/5. There is something that might resemble a beat frequency pattern (the really high peaks) but it's very rough and will sound more like noise, if you could hear such low frequencies.

This is due to really poorly picked frequencies in the problem. To talk about beat frequency, you want two signals with a small difference which is also noticeably different from the their frequencies. So 1000/1002 Hz would be a good pair, 3/5 Hz not really good.

First let's look at this:

This is the combination of 50 Hz and 51 Hz signal. The rapid oscillations up and down are what you're going to hear as frequency of the sound (it will be 50.5 Hz). The big sine wave that is formed around the graph is what you're going to hear as intensity - it will be increasing from zero to loud and back to zero once each second.

Now, if you go to some higher freq, like 1200/1202, you get an even more obvious picture:

The oscillations are so close to each other here that you don't really see them. The big wave is just a sound with a pitch fo 1201 Hz going from quite to loud and quite again twice a second. (also, ignore the white space in the solid regions - it's just the graphing program averaging things, it should be equally 'solid' everywhere)

Now if we introduce a third signal, things get more complicated. Let's see what 1200/1202/1204 looks like:

As you can see, we don't have such a nice patter as we had for two frequencies. We'll still get fluctuations in the intensity, but they'll follow a more complex pattern, something like quiet-loud-quiet-really loud-quiet-loud etc..

And it gets even worse if the difference between each two frequencies is different, like 1200/1202/1205.

As you can see, you're dealing with 3 separate peak intensities here and you're not going to completely quiet state either.
While the differences between the different peaks can be difference between the original frequencies, it's not clear what you would like to call 'beat frequency' in that case. Is it any change of increasing to decreasing intensity? Is it between the loudest peaks? Or something else?

All this goes a bit further than intro physics, so I'm not sure why they are bothering with the 3 signals problem. But the problem is deficient in so many ways that I really doubt the writer was paying attention while he was creating the question.

 

[MedPR]

perhaps because they split it in to two levels, the floor and balcony.

floor is 5 hz, balcony is 4 and 2.

so you can either go 6-5 or 5-6. since it's absolute value it doesn't matter.

But why would you add 4 and 2? If anything you would do 4-2 and get 2.

 

[SaintJude]

Let's let this thread die for now, for this question may be flawed. I just e-mailed Kaplan asking about this question and I'll get back to you guys once they reply.

 

[chiddler]

But why would you add 4 and 2? If anything you would do 4-2 and get 2.

i think you're right. first thought was to add them because i considered both of them from the same source, but direction has nothing to do with it

 

[MedPR]

i think you're right. first thought was to add them because i considered both of them from the same source, but direction has nothing to do with it

Yea, you would definitely subtract it on odd seconds (1, 3, 5, etc). I'm not sure how you would quantify it on even seconds though.. Since every 2 seconds both levels would be clapping at the same time..