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Asked by jhajuhi19 | 24 Nov, 2020, 05:30: AM
answered-by-expert Expert Answer
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 Thiyagarajan K | 24 Nov, 2020, 11:09: AM

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