Two sounds, one of 200 Hz and one of 194 Hz occur at the same time. What beat frequency do you hear? Show your calculations
I'm not looking for someone to do my homework for me. I just don't know what formula to use to figure it out.
http://en.wikipedia.org/wiki/Beat_%28acoustics%29
basically you have
197 Hz + 3 Hz
and
197 Hz - 3 hz
use
sin (p) + sin (q) = 2 sin(1/2)(p+q) cos(1/2)(p-q)
assume 2 pi t everywhere in those trig functions
here p = 200 and q = 194
(1/2) (p+q) = our mean of 197
(1/2)(p-q) = 3
so
sin p + sin q = 2 sin 197* 2 pit sin 3* 2 pi t
so the beat signal is
sin 3 * 2 pi t
f = 3 Hz
sin p + sin q = 2 sin 197* 2 pit cos 3* 2 pi t
so the beat signal is
cos 3 * 2 pi t
6
The envelope frequency is therefore 3 Hz but we will hear a maximum of the 197 HZ signal twice per period of the envelope, thus we will hear the original difference frequency of 6 Hz
To find the beat frequency between two sounds, you can use the formula:
Beat frequency (fbeat) = absolute value (f1 - f2)
Where f1 is the frequency of one sound and f2 is the frequency of the other sound.
In this case, the frequency of one sound is 200 Hz (f1) and the frequency of the other sound is 194 Hz (f2).
Substituting the values into the formula, we have:
fbeat = |200 Hz - 194 Hz|
Calculating the difference between the frequencies:
fbeat = |6 Hz|
The absolute value of 6 Hz is 6 Hz.
Therefore, the beat frequency you would hear is 6 Hz.