Diffraction occurs for all types of waves, including sound...

Diffraction occurs for all types of waves, including sound waves. High-frequency sound from a distant source with wavelength 9.00 cm passes through a slit 12.0 cm wide. A microphone is placed 8.00 m directly in front of the center of the slit, corresponding to point $O$ in Fig. 36.5a. The microphone is then moved in a direction perpendicular to the line from the center of the slit to point $O$. At what distances from $O$ will the intensity detected by the microphone be zero?

Key Concepts

Diffraction

Diffraction is the phenomenon in which waves bend around obstacles or spread as they pass through small openings. This behavior reveals the wave nature of many physical phenomena, including sound, light, and water waves, and it becomes especially noticeable when the size of the aperture or obstacle is comparable to the wavelength of the wave.

Single?Slit Diffraction

Single-slit diffraction refers to the interference pattern produced when waves pass through a narrow slit. The wavefront emerging from the slit spreads out and interferes with itself, leading to regions of constructive and destructive interference. The pattern typically features a central maximum with successive side minima and maxima whose positions can be predicted by a mathematical relation involving the slit width and wavelength.

Interference and Phase Difference

Interference occurs when two or more waves superimpose to form a resultant wave. The constructive or destructive nature of the interference depends on the relative phase difference between the waves. In the context of diffraction, the different parts of the slit can be thought of as secondary wave sources that interfere with one another, resulting in intensity variations across the observation screen.

Fraunhofer Diffraction Approximation

Fraunhofer diffraction applies to situations where the source of the waves and the observation point are effectively at infinite distances from the diffracting aperture, or when lenses are used to simulate such conditions. Under this approximation, the angular positions of minima and maxima in the diffraction pattern can be described by simple equations, making it easier to relate physical dimensions (like slit width and wavelength) to measurable distances on a screen.

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