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Bears, BEATS, Battlestar Galactica
Bears, BEATS, Battlestar Galactica
But how do I hear a beat?
So, when the frequency difference is large, you hear the waves as two distinct sounds, instead of one with a large amplitude.
What happens is that when two sound waves are interfering, they will being to interfere constructively for a couple cycles, then they will begin to interfere destructively. They will repeat this cycle, of being of of phase then in phase. The resultant wave from these two will be heard as a beating effect.
understanding
beats and interference
BEATS
We had defined areas of constructive and destructive interference as being separated by intervals of space, but what if they were separated by time!?
When you hear waves that have different frequencies, you are actually hearing the amplitude increase and decrease.
THIS IS A BEAT: The rate at which the amplitude varies proportional to the difference in frequency!
Mathematics of Beats
How do I calculate the beat frequency though??
Beat frequency= (frequency of one wave)- (frequency of another)
Other important equations:
Math of beats in one direction with different frequencies but the same amplitude
s1=scos (k1x- w1t)
s2=scos(k2x-w2t)
when you add these equations together and simplify you end with:
stotal(0,t)=2scos(((w1+w2)/2)t*cos (((w1-w2)/2)t)
Equations of Interference
Question 1:
If
d1= path length from source 1
d2= path length from source 2
(where m and n are integers)
FOR A CONSTRUCTIVE WAVE:
d2-d1= (n-m)
FOR A DESTRUCTIVE WAVE:
d2-d1=(n=0.5)
***Here, the regions of constructive/destructive interference are separated by regions of space. These equations are defined as the integers reference the space between waves.
If the lowest key on a piano has a frequency of about 27.5Hz and another key on the piano has a frequency of 41.2Hz, what is the beat frequency?
First, Interference
To understand BEATS, we first must understand the concept behind Interference.
CONSTRUCTIVE: The amplitude of waves add. The path difference between waves is an integer multiple of the wavelength.
DESTRUCTIVE: When the waves are perfectly out of interference. This is when one path is an integer number of wavelengths and the other is a half-integer multiple.
Answer: 13.7 Hz
Explanation:
41.2 - 27.5 = 13.7
It's that easy!!!
*** note, human ears can only detect beat frequencies of 7Hz or less***