Concept explainers
Consider an array of parallel wires with uniform spacing of 1.30 cm between centers. In air at 20.0°C, ultrasound with a frequency of 37.2 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.
(a)
Answer to Problem 38.27P
Explanation of Solution
Given info: Temperature of air is
The wavelength for a diffraction grating can be given as,
Here,
Substitute
The condition for the bright fringe in diffraction can be given as,
Here,
Substitute
The maximum number of direction possible can be given as,
Here,
Substitute
Thus, the number of directions on the other side of the array for maximum intensity is three.
Conclusion:
Therefore, the number of directions on the other side of the array for maximum intensity is three.
(b)
Answer to Problem 38.27P
Explanation of Solution
Given info: Temperature of air is
The condition for a diffraction grating as in equation (1) can be given as,
Rearrange the above expression for
Substitute
As the range of sine function is
Substitute
Thus,
Substitute
Thus,
Substitute
Thus,
Conclusion:
Therefore, the angle for each of the directions relative to the direction of the incident beam is
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