YF_ISM_35

# YF_ISM_35 - INTERFERENCE 35 35.1. 35.2. IDENTIFY: Compare...

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35-1 I NTERFERENCE 35.1. IDENTIFY: Compare the path difference to the wavelength. SET UP: The separation between sources is 5.00 m, so for points between the sources the largest possible path difference is 5.00 m. EXECUTE: (a) For constructive interference the path difference is ,0 , 1 , 2 , . . . mm λ =±± Thus only the path difference of zero is possible. This occurs midway between the two sources, 2.50 m from A. (b) For destructive interference the path difference is 1 2 ( ) , 0, 1, 2,. .. += ± ± A path difference of 2 3.00 / ±= m is possible but a path difference as large as 3 / 2 9.00 = m is not possible. For a point a distance x from A and 5.00 from xB the path difference is (5.00 m ). (5.00 m ) 3.00 m gives 4.00 m. xx x −− = + = (5.00 m ) 3.00 m gives 1.00 m x = = . EVALUATE: The point of constructive interference is midway between the points of destructive interference. 35.2. IDENTIFY: For destructive interference the path difference is 1 2 ( ), 0 ,1 ,2 , ± ± . The longest wavelength is for 0 m = . For constructive interference the path difference is , 0, 1, 2, The longest wavelength is for 1 m = . SET UP: The path difference is 120 m. EXECUTE: (a) For destructive interference 120 m 240 m. 2 = = (b) The longest wavelength for constructive interference is 120 m. = EVALUATE: The path difference doesn't depend on the distance of point Q from B . 35.3. IDENTIFY: Use cf = to calculate the wavelength of the transmitted waves. Compare the difference in the distance from A to P and from B to P. For constructive interference this path difference is an integer multiple of the wavelength. SET UP: Consider Figure 35.3 The distance of point P from each coherent source is A rx = and 9.00 m . B =− Figure 35.3 EXECUTE: The path difference is 9.00 m 2 . BA rr x −= 0, 1, 2, rrmm = ± ± 8 6 2.998 10 m/s 2.50 m 120 10 Hz c f × == = × Thus 9.00 m 2 (2.50 m) xm and 9.00 m (2.50 m) 4.50 m (1.25 m) . 2 m x must lie in the range 0 to 9.00 m since P is said to be between the two antennas. 0 m = gives 4.50 m x = 1 m =+ gives 4.50 m 1.25 m 3.25 m x =−= 2 m gives 4.50 m 2.50 m 2.00 m x 3 m gives 4.50 m 3.75 m 0.75 m x 1 m gives 4.50 m 1.25 m 5.75 m x =+= 2 m gives 4.50 m 2.50 m 7.00 m x 3 m gives 4.50 m 3.75 m 8.25 m x 35

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35-2 Chapter 35 All other values of m give values of x out of the allowed range. Constructive interference will occur for 0.75 m, 2.00 m, 3.25 m, 4.50 m, 5.75 m, 7.00 m, and 8.25 m. x = EVALUATE: Constructive interference occurs at the midpoint between the two sources since that point is the same distance from each source. The other points of constructive interference are symmetrically placed relative to this point. 35.4. IDENTIFY: For constructive interference the path difference d is related to λ by , 0,1,2, dmm == For destructive interference 1 2 ( ) , 0,1,2, dm m =+ = SET UP: 2040 nm d = EXECUTE: (a) The brightest wavelengths are when constructive interference occurs: 34 5 2040nm 680 nm, 510 nm and 2040 nm 408 nm. 5 mm d m λλ = = (b) The path-length difference is the same, so the wavelengths are the same as part (a).
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## This note was uploaded on 03/14/2012 for the course MAE 162D taught by Professor Shaefer during the Spring '11 term at UCLA.

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YF_ISM_35 - INTERFERENCE 35 35.1. 35.2. IDENTIFY: Compare...

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