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 $9.00 \mathrm{~cm}$ passes through a slit $12.0 \mathrm{~cm}$ wide. A microphone is placed $8.00 \mathrm{~m}$ directly in front of the center of the slit, corresponding to point $O$ in Fig. 36.5 a. 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 where waves bend around obstacles or spread out after passing through narrow apertures. This behavior is intrinsic to all types of waves, and it is particularly noticeable when the size of the aperture is comparable to the wavelength of the wave, leading to observable interference effects.

Single-Slit Diffraction

Single-slit diffraction refers to the pattern produced when a monochromatic wave passes through a narrow slit. The wavefronts diffract or spread out, and the superposition of these diverging waves results in an interference pattern marked by a central bright maximum and a series of alternating minima and secondary maxima on either side.

Fraunhofer Diffraction

Fraunhofer diffraction describes the far-field limit of diffraction, where the light or sound waves are essentially parallel when they arrive at the observation screen. This approximation simplifies the analysis, as it allows the diffraction pattern to be described using simple relationships between the slit dimensions, the wavelength, and the angular positions of the interference minima and maxima.

Interference Minima Condition

The interference minima in a single-slit diffraction pattern occur when waves emanating from different parts of the slit arrive at a given point with a phase difference that leads to complete destructive interference. Mathematically, this condition is expressed as a*sin(?) = m*?, where 'a' is the width of the slit, '?' is the wavelength, '?' is the diffraction angle, and 'm' is a nonzero integer corresponding to the order of the minimum.

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