How to Calculate Error on Beat Frequency?

  • Thread starter Thread starter belgin fish
  • Start date Start date
  • Tags Tags
    Error Frequency
AI Thread Summary
To calculate the error on a beat frequency, it's essential to understand that the beat frequency is the difference between two frequencies. For example, if two tones at 1000 Hz and 1100 Hz are mixed, the beat frequency is determined by subtracting the lower frequency from the higher one. The accuracy of the frequencies affects the beat frequency's error range; if both frequencies have an error of ±10 Hz, the beat frequency could vary between 80 Hz and 120 Hz, resulting in an error of ±20 Hz. Using a differential equation is unnecessary for such straightforward calculations, which are best approached with basic arithmetic. Accurate error calculation relies on knowing the frequencies and their respective uncertainties.
belgin fish
Messages
1
Reaction score
0
I'm being asked to calculate the error on a beat frequency. The beat frequency was found to be 1/20.0s



The equation given is
atlxz4.png





The thing is I am not really sure where to go from there or how to get the derivative of that, any help or pointing me in the right direction would be much appreciated.
 
Physics news on Phys.org
Welcome to PF, Belgin.

You can only use that formula if you have the formula for f as a function of T and the error in T. It actually doesn't look like the right formula to me.

The beat frequency is the difference between two frequencies. Say you have two tones at 1000 Hz and 1100 Hz mixing together in your ear. You will hear 1000, 1100, the "beat" or difference between them and perhaps the sum. You would do 1100 - 1000 = 100 to calculate the beat frequency. If the accuracy on the 1100 and the 1000 is ± 10 Hz, then the beat could be anywhere from
(1100 - 10) - (1000 + 10) = 80 Hz to (1100+10) - (1000 - 10) = 120 Hz
so you would say it is 100 ± 20 Hz. I don't think it makes sense to use the differential equation in such a simple case - save it for a situation where you have multiplying at least.
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
View full post »
Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

Beat frequency and Doppler shift
Replies
3
Views
3K
How close should frequencies be to show 'beating'?
Replies
13
Views
2K
Wave interference, "beats" problem
Replies
19
Views
1K
Travelling towards a Canyon Wall: Calculating Beat Frequency
Replies
3
Views
2K
A question about wave motion and beat frequency
Replies
43
Views
6K
Solving Beat Frequency with Tuning Forks: f2 = f1 ± fb
Replies
6
Views
5K
How do you find speed given the beat frequency?
Replies
3
Views
3K
Flute player initial frequency?
Replies
7
Views
8K
Device that detect waves in a frequency range and beats
Replies
1
Views
2K
Error propagation leads to different uncertainties, which do I choose?
Replies
15
Views
2K

Hot Threads

Recent Insights

Back
Top