Physics Problem

[uNiT 0]

My friend recently took a physics test, and was stumped on a problem. It was a random problem not related to their current subjects, and here it is:

Problem:
You hear a tone and you recognize the frequency as 243Hz. You hear another one, but don't know the frequency, but you count the beats of the combined tones as 24 beats in 3 seconds. What is the frequency of the second tone?

(In formula sheet, you have: f_beat = |f1 - f2| )

He came up with 235.
The closest choices on the answer sheet were 264 and 226.

Here was my attempt at solving..

fbeat = |f1 - f2|fbeat = |243 - x|
fbeat = fb

Remember that Frequency = Occurances / Time; and that Hz is over a period of 1 second so..

fb = O/C
fb = 24/3s
fb = 8bps or fb = 8hz

so

8hz = | 243 - 235 |
x = 235?

But then we see thats wrong, proving me to be stupid. So lets say there was a second in between the beats.

fb = O/C
fb = 24/2
fb = 12hz

12hz = 243 - 239

Still doesn't work. Hmm...Well but lets say the teacher errored in his positioning of the absolute values. In which case we could wonder if..

-12hz = 243 - 255

255 isnt on the answer sheet either? So damn...what about averages?


say fb = average of f1 - f2.
8 = 243 - f2 / 2
243 - 227 = 16
x = 227?

So ive come up with x = 235, 239, 255, and 227.

227 is very close to 226.

Regardless, I think this is the professors error

Any ideas?

[dserban 0]

Well, I'm not going to crunch any numbers, but I am going to explain the underlying physical phaenomena in layman's terms.Seen as a single-frequency sound consists of just a wave like any other wave (with its peaks and troughs), if you have two such waves (tones) going on at the same time, sooner or later their peaks are going to happen at the same time. That's when they reinforce each other, and the audible effect is a short pulse. After that, they continue interfering with each other until the first wave's peak coincides with the second wave's trough. At this point, of course, the two sounds are going to cancel each other out.This successive reinforcing and canceling each other out of the two waves therefore happens with a certain frequency, which in your case is 8 Hz (24 beats in 3 seconds).Maybe I'm explaining the obvious, I don't know, but if you think of the problem in these qualitative terms, the numerical solution immediately jumps out at you.

Edited September 15, 2007 by dserban (see edit history)

[uNiT 0]

Ah that makes much more sense...Thanks, I'll let him know this. =]

[xboxrulz1405241485 0]

wow, this is grade 11 physics, but I don't quite remember.I'll c if I can solve it when I have the time....xboxrulz