Question

what is beats..explain with mathematical forms​

Answer 1

Explanation:

According to the superposition principle, if at a certain position the two waves are given by, let say,

ya(t)=Asin(2πfat)

ya(t)=Asin(2πfat)

yb(t)=−Asin(2πfbt)

yb(t)=−Asin(2πfbt)

then the total wave will be

ya(t)+yb(t)=[2Asin(12(2π)(fa−fb)t]cos12(2π)(fa+fb)t

ya(t)+yb(t)=[2Asin(12(2π)(fa−fb)t]cos12(2π)(fa+fb)t

Now, my question is, when grouping the terms in this expression, why do you say that the sin(12(2π)(fa−fb)tsin(12(2π)(fa−fb)t is the amplitude factor and not the cos12(2π)(fa+fb)tcos12(2π)(fa+fb)t. How can you know that it's the sine not the cosine that is varying the amplitude.

Edit: my real question is that why is it the fa−fbfa−fb not the fa+fbfa+fb term that is modulating the amplitude..

i hope this is help you....