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 wave-length 9.00 $\mathrm{cm}$ passes through a narrow slit 12.0 $\mathrm{cm}$ wide. A microphone is placed 40.0 $\mathrm{cm}$ directly in front of the center of the slit, corresponding to point $O$ in Fig. 36.5 $\mathrm{a}$ . 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?

Diffraction occurs for all types of waves, including sound waves. High-frequency sound from a distant source with wave-length 9.00 $\mathrm{cm}$ passes through a narrow slit 12.0 $\mathrm{cm}$ wide. A
microphone is placed 40.0 $\mathrm{cm}$ directly in front of the center of the slit, corresponding to point $O$ in Fig. 36.5 $\mathrm{a}$ . 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

Fraunhofer Diffraction

Fraunhofer diffraction refers to the far-field approximation of diffraction, where the sources of the waves are effectively at infinity or the wave fronts are essentially planar. In this regime, the pattern observed is the Fourier transform of the aperture, and the simple relationship for the minima positions becomes applicable. The analysis of the diffraction pattern, in this case with the microphone at a known distance, typically relies on this approximation.

Interference Condition for Diffraction Minima

The positions of zero intensity, or minima, in a single?slit diffraction pattern are determined by the condition a sin ? = m?, where a is the width of the slit, ? is the wavelength of the wave, and m is a nonzero integer (m = ±1, ±2, ...). This formula expresses the path difference required for destructive interference among the waves emerging from different parts of the slit.

Wave Nature of Sound

Sound waves exhibit properties similar to other wave types, including diffraction, interference, and reflection. The wave behavior of sound is characterized by its frequency and wavelength, and phenomena such as diffraction occur when sound waves encounter obstacles or pass through openings that are comparable in size to their wavelength.

Diffraction

Diffraction is the phenomenon in which waves bend around obstacles or spread out when they pass through narrow openings. This behavior is inherent to all types of waves, including sound, light, and water waves, and is a fundamental demonstration of the wave nature of these phenomena.

Single?Slit Diffraction

Single?slit diffraction occurs when waves pass through a narrow aperture and interfere with themselves, creating a pattern of bright and dark regions. The emerging waves from different parts of the slit combine constructively and destructively at various angles, which results in the distinctive intensity pattern observed on the detection screen.

Please give Ace some feedback