Four sound waves are to be sent through the same tube of air, in the same direction: s_1(x,t)=(9.00nm)cos(2pix−700pit) s_2(x,t)=(9.00nm)cos(2pix−700pit+0.7pi) s_3(x,t)=(9.00nm)cos(2pix700pit+pi) s_4(x,t)=(9.00nm)cos(2pix−700pit+1.7pi) What is the amplitude of the resultant wave?

trapskrumcu 2022-09-25 Answered
Four sound waves are to be sent through the same tube of air, in the same direction:
s 1 ( x , t ) = ( 9.00 n m ) cos ( 2 π x 700 π t )
s 2 ( x , t ) = ( 9.00 n m ) cos ( 2 π x 700 π t + 0.7 π )
s 3 ( x , t ) = ( 9.00 n m ) cos ( 2 π x 700 π t + π )
s 4 ( x , t ) = ( 9.00 n m ) cos ( 2 π x 700 π t + 1.7 π )
What is the amplitude of the resultant wave?
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Answers (1)

cercimw
Answered 2022-09-26 Author has 8 answers
The sound waves are
s 1 ( x , t ) = ( 9.00 n m ) cos ( 2 π x 700 π t )
s 2 ( x , t ) = ( 9.00 n m ) cos ( 2 π x 700 π t + 0.7 π )
s 3 ( x , t ) = ( 9.00 n m ) cos ( 2 π x 700 π t + π )
s 4 ( x , t ) = ( 9.00 n m ) cos ( 2 π x 700 π t + 1.7 π )
From super position The net wave is
S ( x , t ) = s 1 ( x , t ) + s 2 ( x , t ) + s 3 ( x , t ) + s 4 ( x , t )
By using the sum identities
cos x + cos y = 2 cos ( x + y 2 ) cos ( x y 2 )
S ( x , t ) = ( s 1 ( x , t ) + s 3 ( x , t ) ) + ( s 2 ( x , t ) + s 4 ( x , t ) )
= ( 18 n m ) cos ( 2 π x 700 π t + π / 2 ) cos ( π / 2 ) + ( 18 n m ) cos ( 2 π x 700 π t + 1.2 π ) cos ( π / 2 ) = 0
Result:
S=0
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