4 . Two waves are given as W1 �11cos ( 2� t� 0.1 ) and W2 �13cos ( 2� t� 0.3 ) respectively , where W
1 and W
2 represent the amplitudes of the two waves respectively . t represents time in seconds . The total amplitude W is given by W �W1� W2.
( a ) Find the period of W
2
.
2�ti
It is given that W1� W2 � Re ( e ( z � w)) , z , w� . w is in the form
( b ) Find the expression of z� w.
( c ) Express the following in the form r( cos� � isin �)
:
0.3i re � .
[ 2 ]
[ 3 ]
( i ) z ( ii ) w
( d ) It is given that
i z �w � Le � . Find
[ 2 ]
( i ) |
L ; |
( ii ) |
� . |
[ 6 ] |
( e ) |
2�ti
Using
W1�
W2
�
Re ( e
( z
� w))
, express W in the form
Acos (
Bt
�
C)
, A ,
|
B , C � |
. |
[ 3 ] |
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