Sound Diffraction Examples

1. Sound Diffraction Examples Worksheet
2. Sound Diffraction Examples Science

Learning Objectives

By the end of this section, you will be able to:

• Definition of diffraction in the Definitions.net dictionary. Meaning of diffraction. What does diffraction mean? Information and translations of diffraction in the most comprehensive dictionary.
• Flexible Optical B.V. (aka OKO Technologies or OKOTech) develops, manufactures and delivers adaptive optical systems for adaptive wavefront correction and generation in scientific, industrial.
• Producing vowel sounds requires resonance more than producing consonants. Make your sounds talk using EQ and formant frequencies.

Suppose there is a dark room and through the window, there is a small hole. When light enters through tiny hole we see that through the small hole light enters but instead of just bright light, we.

• Discuss the single slit diffraction pattern.

Figure 1. (a) Single slit diffraction pattern. Monochromatic light passing through a single slit has a central maximum and many smaller and dimmer maxima on either side. The central maximum is six times higher than shown. (b) The drawing shows the bright central maximum and dimmer and thinner maxima on either side.

Light passing through a single slit forms a diffraction pattern somewhat different from those formed by double slits or diffraction gratings. Figure 1 shows a single slit diffraction pattern. Note that the central maximum is larger than those on either side, and that the intensity decreases rapidly on either side. In contrast, a diffraction grating produces evenly spaced lines that dim slowly on either side of center.

The analysis of single slit diffraction is illustrated in Figure 2. Here we consider light coming from different parts of the same slit. According to Huygens's principle, every part of the wavefront in the slit emits wavelets. These are like rays that start out in phase and head in all directions. (Each ray is perpendicular to the wavefront of a wavelet.) Assuming the screen is very far away compared with the size of the slit, rays heading toward a common destination are nearly parallel. When they travel straight ahead, as in Figure 2a, they remain in phase, and a central maximum is obtained. However, when rays travel at an angle θ relative to the original direction of the beam, each travels a different distance to a common location, and they can arrive in or out of phase. In Figure 2b, the ray from the bottom travels a distance of one wavelength λ farther than the ray from the top. Thus a ray from the center travels a distance λ/2 farther than the one on the left, arrives out of phase, and interferes destructively. A ray from slightly above the center and one from slightly above the bottom will also cancel one another. In fact, each ray from the slit will have another to interfere destructively, and a minimum in intensity will occur at this angle. There will be another minimum at the same angle to the right of the incident direction of the light.

In Figure 2 we see that light passing through a single slit is diffracted in all directions and may interfere constructively or destructively, depending on the angle. The difference in path length for rays from either side of the slit is seen to be D sin θ.

Figure 3. A graph of single slit diffraction intensity showing the central maximum to be wider and much more intense than those to the sides. In fact the central maximum is six times higher than shown here.

At the larger angle shown in Figure 2c, the path lengths differ by 3λ/2 for rays from the top and bottom of the slit. One ray travels a distance λ different from the ray from the bottom and arrives in phase, interfering constructively. Two rays, each from slightly above those two, will also add constructively. Most rays from the slit will have another to interfere with constructively, and a maximum in intensity will occur at this angle. However, all rays do not interfere constructively for this situation, and so the maximum is not as intense as the central maximum. Finally, in Figure 2d, the angle shown is large enough to produce a second minimum. As seen in the figure, the difference in path length for rays from either side of the slit is D sin θ, and we see that a destructive minimum is obtained when this distance is an integral multiple of the wavelength.

Thus, to obtain destructive interference for a single slit, D sin θ = mλ, for m = 1,−1,2,−2,3, . . . (destructive), where D is the slit width, λ is the light's wavelength, θ is the angle relative to the original direction of the light, and m is the order of the minimum. Figure 3 shows a graph of intensity for single slit interference, and it is apparent that the maxima on either side of the central maximum are much less intense and not as wide. This is consistent with the illustration in Figure 1b.

Example 1. Calculating Single Slit Diffraction

Visible light of wavelength 550 nm falls on a single slit and produces its second diffraction minimum at an angle of 45.0º relative to the incident direction of the light.

1. What is the width of the slit?
2. At what angle is the first minimum produced?

A graph of the single slit diffraction pattern is analyzed in this example.

Strategy

From the given information, and assuming the screen is far away from the slit, we can use the equation D sin θ = mλ first to find D, and again to find the angle for the first minimum θ₁.

Solution for Part 1

We are given that λ = 550 nm, m = 2, and θ₂ = 45.0º. Solving the equation D sin θ = mλ for D and substituting known values gives

[latex]begin{array}{lll}D&=&frac{mlambda}{sintheta_2}=frac{2left(550text{ nm}right)}{sin45.0^{circ}}text{ }&=&frac{1100times10^{-9}}{0.707}text{ }&=&1.56times10^{-6}end{array}[/latex]

Solution for Part 2

Solving the equation D sin θ = mλ for sin θ₁ and substituting the known values gives

[latex]displaystylesintheta_1=frac{mlambda}{D}=frac{1left(550times10^{-9}text{ m}right)}{1.56times10^{-6}text{ m}}[/latex]

Thus the angle θ₁ is θ₁ = sin⁻¹ 0.354 = 20.7º.

Discussion

We see that the slit is narrow (it is only a few times greater than the wavelength of light). This is consistent with the fact that light must interact with an object comparable in size to its wavelength in order to exhibit significant wave effects such as this single slit diffraction pattern. We also see that the central maximum extends 20.7º on either side of the original beam, for a width of about 41º. The angle between the first and second minima is only about 24º(45.0º − 20.7º). Thus the second maximum is only about half as wide as the central maximum.

Section Summary

• A single slit produces an interference pattern characterized by a broad central maximum with narrower and dimmer maxima to the sides.
• There is destructive interference for a single slit when D sin θ = mλ, (form = 1,–1,2,–2,3, . . .), where D is the slit width, λ is the light's wavelength, θ is the angle relative to the original direction of the light, and m is the order of the minimum. Note that there is no m = 0 minimum.

Conceptual Questions

1. As the width of the slit producing a single-slit diffraction pattern is reduced, how will the diffraction pattern produced change?

Problems & Exercises

1. (a) At what angle is the first minimum for 550-nm light falling on a single slit of width 1.00 μm? (b) Will there be a second minimum?
2. (a) Calculate the angle at which a 2.00-μm-wide slit produces its first minimum for 410-nm violet light. (b) Where is the first minimum for 700-nm red light?
3. (a) How wide is a single slit that produces its first minimum for 633-nm light at an angle of 28.0º? (b) At what angle will the second minimum be?
4. (a) What is the width of a single slit that produces its first minimum at 60.0º for 600-nm light? (b) Find the wavelength of light that has its first minimum at 62.0º.
5. Find the wavelength of light that has its third minimum at an angle of 48.6º when it falls on a single slit of width 3.00 μm.
6. Calculate the wavelength of light that produces its first minimum at an angle of 36.9º when falling on a single slit of width 1.00 μm.
7. (a) Sodium vapor light averaging 589 nm in wavelength falls on a single slit of width 7.50 μm. At what angle does it produces its second minimum? (b) What is the highest-order minimum produced?
8. (a) Find the angle of the third diffraction minimum for 633-nm light falling on a slit of width 20.0 μm. (b) What slit width would place this minimum at 85.0º?
9. (a) Find the angle between the first minima for the two sodium vapor lines, which have wavelengths of 589.1 and 589.6 nm, when they fall upon a single slit of width 2.00 μm. (b) What is the distance between these minima if the diffraction pattern falls on a screen 1.00 m from the slit? (c) Discuss the ease or difficulty of measuring such a distance.
10. (a) What is the minimum width of a single slit (in multiples of λ) that will produce a first minimum for a wavelength λ? (b) What is its minimum width if it produces 50 minima? (c) 1000 minima?
11. (a) If a single slit produces a first minimum at 14.5º, at what angle is the second-order minimum? (b) What is the angle of the third-order minimum? (c) Is there a fourth-order minimum? (d) Use your answers to illustrate how the angular width of the central maximum is about twice the angular width of the next maximum (which is the angle between the first and second minima).
12. A double slit produces a diffraction pattern that is a combination of single and double slit interference. Find the ratio of the width of the slits to the separation between them, if the first minimum of the single slit pattern falls on the fifth maximum of the double slit pattern. (This will greatly reduce the intensity of the fifth maximum.)
13. Integrated Concepts. A water break at the entrance to a harbor consists of a rock barrier with a 50.0-m-wide opening. Ocean waves of 20.0-m wavelength approach the opening straight on. At what angle to the incident direction are the boats inside the harbor most protected against wave action?
14. Integrated Concepts. An aircraft maintenance technician walks past a tall hangar door that acts like a single slit for sound entering the hangar. Outside the door, on a line perpendicular to the opening in the door, a jet engine makes a 600-Hz sound. At what angle with the door will the technician observe the first minimum in sound intensity if the vertical opening is 0.800 m wide and the speed of sound is 340 m/s?

Glossary

destructive interference for a single slit: occurs when D sin θ = mλ, (form=1,–1,2,–2,3, . . .), where D is the slit width, λ is the light's wavelength, θ is the angle relative to the original direction of the light, and m is the order of the minimum

Selected Solutions to Problems & Exercises

1. (a) 33.4º; (b) No

3. (a) 1.35 × 10⁻⁶ m; (b) 69.9º

5. 750 nm

7. (a) 9.04º; (b) 12

9. (a) 0.0150º; (b) 0.262 mm; (c) This distance is not easily measured by human eye, but under a microscope or magnifying glass it is quite easily measurable.

11. (a) 30.1º; (b) 48.7º; (c) No; (d) 2θ₁ = (2)(14.5º) = 29º, θ₂ − θ₁ = 30.05º − 14.5º = 15.56º. Thus, 29º ≈ (2)(15.56º) = 31.1º.

13. 23.6º and 53.1º

DOI:

Keywords:

Abstract

As the object of research, sensor unit as a multiphase mechanical construction in the operating conditions of hypersonic aircraft flight is exposed to actions of powerful external disturbances such as: ultra-high temperature – more than 2000 ºC, vibration, shock N-wave, acoustic penetrating radiation. Less harmful disturbances cause additional measurement errors of characteristics of the flight product. Clarification of the nature and origin in time and space of these errors is one of the most important tasks of navigation.

Precisely delineated investigated phenomenon enables combat the negative influence of external disturbing factors by passive, active or autocompensation methods depending on character of the sensor error – methodological or instrumental.

The obtained result confirms the presence of powerful and fluid motive flow with a spatial structure in a liquid-phase components of component base, which, in combination with generated sound waves form a zone of concentration of sound energy and, in accordance, development of three-dimensional turbulent fluid, and explains the emergence of areas of passive energy, in which is virtually absent turbulence.

The expected effect of an efficient fight against the negative impact of penetrating sound radiation is based on eliminating an effect of aberrations and forming a powerful energy zones (zones of caustic surfaces), technical implementation of which in each case may have its advantages and disadvantages.

References

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Karachun, V., Mel'nick, V., Korobiichuk, I., Nowicki, M., Szewczyk, R., Kobzar, S. (2016, February 26). The Additional Error of Inertial Sensors Induced by Hypersonic Flight Conditions. Sensors, 16 (3), 299. doi:10.3390/s16030299

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Copyright (c) 2016 Володимир Володимирович Карачун, Вікторія Миколаївна Мельник, Сергій Вікторович Фесенко

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