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..


Any ideas?

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.

This post has been edited by dserban: Sep 15 2007, 08:52 PM

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

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