Understanding how to find the fundamental fequency when given the beat frequency?

[noisyhose933]

1) Two tuning forks are sounded together. One is of frequency 512 Hz and the other is of frequency 520 Hz. Determine: a) the beat frequency

for part a) its F2 - F1 = FB (beat frequency) to find the beat frequency so its 520 - 512 = 8 Hz, what determines which frequency is F2 and what determmines which frequency is F1?, because if i get this wrong i could have the wrong answer, in this case i could get -8Hz

2) A tuning form of requency 256Hz is sounded at the same time as a wire vibrating at the same time as a wire vibrating at its fundamental frequency. 6 beats are heard every second. The prongs of the tuning fork are then lightly loaded with plasticine causing the beat frequency to reduce to 4 beats per second, calculate:

a) the fundamental frequency of the wire and b) the frequency of the loaded tuning fork

b) the frequency of the loaded tuning fork


a) for this question F1 is 256 Hz? i don't know why but i assumed it is F1 and i require to find F2 where the beat frequency is 6 Hz, fo i use F2 - F1 = FB, so F2 - 256 = 6, and F2=262 Hz, this answer is wrong. But i do not know why?

The correct answer involves using the following formula F1 - F2 = FB where F1 is 256 Hz and with some algebra caclulate F2 to find the correct answer but i have never seen this formula before and want to understand its intended use while also being able to identify which frequency i am required to find in a question, in this case i was required to find "F2"

b) for this question i also attempted to apply F2 - F1 = FB but it turned out this was incorrect and again the correct formula to use was F1 - F2 = FB, i also incorrectly identified F1 to be the frequency calculated in part a), in this part i was required to find F1 where F2 was supposed to be the frequency calculated from part a) again where did i go wrong and what is the best way to idnetify the correct frequency to find the desired result please?


Thank you for any help, very much appreciated.

[lunchtime_browser]

1) You choose F1 and F2 so that you get the correct answer. What on earth is a negative frequency? You know before you start that you are looking for an answer which is positive.

2) The tuning fork frequency is 256 Hz and the beat frequency is 6 Hz. So there are TWO possible values for the frequency of the string:

Either
(i) f = (256 - 6) = 250 Hz
In which case FB = (256 - 250) = 6 Hz

Or
(ii) f = (256 + 6) = 262 Hz
In which case FB = (262 - 256) = 6 Hz

Up to this point, you have no way of knowing which it is. To find out, you load the prongs of the fork.
What will that do? It will lower the frequency of the tuning fork slightly, to something a bit less than 256 Hz.

Now you can see that it can't possibly be option (ii).
262 Hz - [something a bit less than 256 Hz] would make FB bigger than 6 Hz and that is not what happens here. FB reduces to 4 Hz.

So we are dealing with option (i) here and the wire frequency f = 250 Hz
(loaded fork frequency - 250) = 4 Hz
loaded fork frequency = (250 + 4) = 254 Hz

The bottom line is that this is all about solving logic problems; not just plugging values into a remembered formula.