Bats emit ultrasound in order to detect prey. Ultrasound has...

Bats emit ultrasound in order to detect prey. Ultrasound has a much smaller wavelength than sound, which improves the resolution of small objects. What is the diameter of the smallest object that forms a diffraction pattern when irradiated by the $8.0 \times 10^{4}-\mathrm{Hz}$ ultrasound from a bat? The first diffraction minimum from the smallest object that still produces diffraction forms at $90^{\circ}$ with respect to the direction of the incident waves.

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Key Concepts

Diffraction

Diffraction is the phenomenon where waves bend around obstacles or spread out after passing through apertures. It is significant when the size of the object or aperture is comparable to the wavelength of the incident wave. The resulting interference pattern, including minima and maxima, encapsulates key information about the wave-object interaction.

Wave Wavelength and Frequency Relationship

The wavelength of a wave is related to its speed and frequency by the equation ? = v/f, where ? is wavelength, v is the speed of the wave, and f is its frequency. This relation is fundamental in calculating the wavelength from a given frequency, which is critical in understanding and predicting diffraction effects.

Diffraction Limit and Resolution

The diffraction limit refers to the fundamental restriction on the resolving power of a wave-based imaging system, arising from the wave nature of the probe. It determines that objects smaller than or comparable to the wavelength of the incident wave do not produce distinct diffraction patterns, thereby setting a limit on the smallest detectable features.

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