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# ⭕ Explain in detail... thanks

Asked by jhajuhi19 24th November 2020, 5:30 AM
if sounds of frequecies f1 and f2 and of same amplitude are combined together , we get the resultant sound as

A cos(2π f1 t ) + A cos ( 2π f2 t ) = 2A cos { 2π [ ( f1 - f2)/2 ] t } cos { 2π [ ( f1 + f2 ) /2 ] t }

Beat sound  =  2A cos { 2π [ ( f1 - f2)/2 ] t }  .......................(1)

at t = 0, we get maximum sound , with amplitude 2A and intensity 4A2

To get Half maximu sound,  Intensity = 2A2 and hence sound level √2 A

Time to get sound level √2 A is calculated as follows

2A cos { 2π [ ( f1 - f2)/2 ] t } = √2 A

2π [ ( f1 - f2)/2 ] t = π/4

t = 1 / [ 4 ( f1 - f2 ) ]  = 1 / [ 4 × 0.05 ] = 5 s
Answered by Expert 24th November 2020, 11:09 AM
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Tags: beats