When two waves of almost equal frequencies f1 and f2 reach at a point simultaneously, what is the time intetval between successive maxima?
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Suppose the two waves have w1 and w2 as their angular frequencies.
Suppose we observe the particle at x=0
The superposition will come out to be
y(net) = y1+y2 = A sin w1*t + A sinw2*t
= 2A sin(w1+w2)/2*t * cos(w1-w2)/2*t
Here, w1 + w2/2 would come out to be a very big value, so it's graph would make the influence on the frequency of the beats.
However, on graph observations, the cos w1-w2/2*t term would make influence on the number of beats and it's time interval for maxima.
Now,for maxima:-
cos (w1-w2)/2*t = +-1
Therefore,
w1-w2/2*t = 0,π,2π,3π.....
2π{f1-f2} / 2 * t = nπ
So,
(f1-f2)*t = n
T = n/f1-f2
So, the time interval between two successive maxima will be 1/f1-f2
So,
Beat frequency = | f1-f2 | beats per second
Hope this helps you !
Suppose we observe the particle at x=0
The superposition will come out to be
y(net) = y1+y2 = A sin w1*t + A sinw2*t
= 2A sin(w1+w2)/2*t * cos(w1-w2)/2*t
Here, w1 + w2/2 would come out to be a very big value, so it's graph would make the influence on the frequency of the beats.
However, on graph observations, the cos w1-w2/2*t term would make influence on the number of beats and it's time interval for maxima.
Now,for maxima:-
cos (w1-w2)/2*t = +-1
Therefore,
w1-w2/2*t = 0,π,2π,3π.....
2π{f1-f2} / 2 * t = nπ
So,
(f1-f2)*t = n
T = n/f1-f2
So, the time interval between two successive maxima will be 1/f1-f2
So,
Beat frequency = | f1-f2 | beats per second
Hope this helps you !
Medivial:
derieve an expression for the frequency of the vibration of the block when the 2 springs of spring constant k1 and k2 are connected in series
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