Consider an array of parallel wires with uniform spacing of 1.62 cm between cent

Question

Consider an array of parallel wires with uniform spacing of 1.62 cm between centers. In air at 20.0°C, ultrasound with a frequency of 42.9 kHz from a distant source is incident perpendicular to the array.

(a) Find the number of directions on the other side of the array in which there is a maximum of intensity.
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(b) Find the angle for each of these directions relative to the direction of the incident beam. (Enter your answers from smallest to largest starting with the first answer blank. Enter NONE in any remaining answer blanks.)
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Consider an array of parallel wires with uniform spacing of 1.62 cm between centers. In air at 20.0°C, ultrasound with a frequency of 42.9 kHz from a distant source is incident perpendicular to the array. (a) Find the number of directions on the other side of the array in which there is a maximum of intensity. (b) Find the angle for each of these directions relative to the direction of the incident beam. (Enter your answers from smallest to largest starting with the first answer blank. Enter NONE in any remaining answer blanks.) Need Help? Read It Talk to a Tutor Need Help -Read lt_1 Talk to a Tutor

Explanation / Answer

a) diffraction grating, wavelength = 343/ 42.9 x 1000

max angle is 90 degrees

m x lambda = d sin theta

m = d/lambda = 0.0162 /(343/ 42.9 x 1000) = 2.026

so rounding down that means m=2

so number of max = 2m+1 = 5

b) m= -2 none
m=-1: theta = sin-1(-1 x (343/42.9 x 1000)/0.0162)= - 29.57 degrees
m= 0: theta = 0
m=1: theta = 29.57 degrees
m=2: none

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