s37 - P37.4 =(a(b(c v 354 m s = = 0 m 177 f 2 000 s1 d si =...

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P37.4 1 354 m s 0.177 m 2000 s v f λ = = = (a) so ( ) and sin d m θ = λ ) ( 0.300 m sin 10.177 m θ = 36.2 θ = ° (b) so and sin d m θ = λ ) ( sin36.2 10.0300 m d ° = 5.08 cm d = (c) so 59 ( ) ( ) 6 1.00 10 m sin36.2 1 λ × ° = 0 nm λ = 8 7 3.00 10 m s 508 THz 5.90 10 m c f λ × = = = × P37.9 Location of A = central maximum, Location of B = first minimum. So, min max 1 1 0 0 20.0 m 2 2 L L y y y d d λ λ Δ = = + = = . Thus, ( ) ( )( ) 3.00 m 150 m 11.3 m 2 20.0 m 40.0 m L d λ = = = . *P37.12 In sin d m θ λ = y d m L λ = m L y d λ = ( ) ( ) 9 3 1633 10 m 3 m s 6.33 mm s 0.3 10 m dy m dL dt d dt λ × = = = × P37.19 (a) From Equation 37.8, ( )( ) ( ) ( ) 2 2 3 3 9 2 2 sin 2 0.850 10 m 2.50 10 m 2 7.95 rad 600 10 m 2.80 m d d y y D yd D π π φ θ λ λ π π φ λ = = + × × = = × (b) ( ) ( ) ( ) 2 2 2 2 max max cos sin cos 2 cos cos sin d I I m d π λ θ φ π π λ θ = = 2 2 max 7.95 rad cos cos 0.453 2 2 I I φ = = = P37.21 (a) We can use sin sin 2sin cos 2 2 2 2 A B A A B + = + B to find the sum of the two sine functions to be ( ) ( ) ( ) ( ) 1 2 1 2 24.0 kN C sin 15 4.5 35.0 cos35.0 19.7 kN C sin 15 4.5 35.0 E E x t E E x t + = + ° + = + ° °
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Thus, the total wave has amplitude 19.7 kN C and has a constant phase difference of 35.0 ° from the first wave. (b) In units of kN/C, the resultant phasor is ( ) ( ) ( ) ( ) 1 2 2 2 1 ˆ ˆ ˆ ˆ ˆ j 12.0 12.0cos70.0 12.0sin70.0 16.1 11.3 11.3 16.1 11.3 at tan 19.7 kN C at 35.0 16.1 R R = + = + ° + = + = + = ° E E E
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