Your Practice Set – Applications and Interpretation for IBDP Mathematics
( e ) It is given that ( i ) L ; i z �w � Le � . Find
( ii ) � .
( f ) Using
S � S � e z � w , express S in the form Asin ( Bt � C) , A , B ,
6i t
1 2
Im ( ( ))
C � .
( g ) Hence , write down the minimum total amplitude .
[ 6 ]
[ 3 ]
[ 1 ]
2 . Two waves are given as W1 �5cos ( �t� 0.9 ) and W2 �7cos ( �t� 1.3 ) 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 ) Write down the amplitude of ( i ) W
1
;
( ii ) W
2
.
( b ) Find the period of W
2
.
�ti
It is given that W1� W2 � Re ( e ( z � w))
, z , w� .
( c ) Find the expression of z� w.
( d ) Express the following in the form r( cos�
� isin �) :
[ 2 ]
[ 2 ]
[ 3 ]
( i ) z ( ii ) w
( e ) It is given that i z �w � Le � . Find
[ 2 ]
( i ) L ; ( ii ) � .
[ 6 ]
�ti
( f ) Using W1� W2 � Re ( e ( z � w))
, express W in the form Acos ( Bt � C) , A , B ,
C � . [ 3 ]
( g ) Hence , find t when W � 0, 1�t
� 2.
[ 2 ]
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