3 . Two sound waves are given as S1 �8cos ( 10t� 0.05 ) and S
2 respectively , where S
1 and
S
2 represent the amplitudes of the two sound waves respectively , in millimetres , and t represents time in seconds . The total amplitude S is given by S � S1� S2 �10cos ( 10t � 0.15 ) .
( a ) For S , write down its
( i ) amplitude ;
It is given that
( ii ) period .
S � e z � w , z , w� .
10ti
2
Re ( ( ))
( b ) Find the expression of z� w.
( c ) Express the following in the form r( cos�
� isin �) :
[ 2 ]
[ 3 ]
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( i ) z
( ii ) w
( d ) It is given that i z �w � Le � . Find
[ 2 ]
( i ) L ;
( ii ) � .
( e ) Express S
2 in the form Acos ( Bt � C) , A , B , C � .
( f ) Hence , find the value of t when S2 � 1.5 , 9.5 �t � 10 .
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[ 3 ]
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