Physics

Physics

Problem

A bat emits an ultrasonic pulse of frequency 40 kHz40\,\text{kHz} as it flies just above the surface of a still pond. The speed of sound in air is 340 m s−1340\,\text{m\,s}^{-1}, while in water it is 1480 m s−11480\,\text{m\,s}^{-1}. a. (a) Calculate the wavelength of the ultrasonic pulse in air. b. (b) Calculate its wavelength in water. c. (c) Show that the ratio of the wavelengths obtained in parts (a) and (b) is equal to the ratio of the speeds of sound in the two media.
Intuitive explanation

This is a wave refraction problem where sound crosses from one medium to another. The key insight is that frequency never changes when a wave crosses a boundary—it's determined by the source—but wavelength and speed do. Use the wave equation v=fλv = f\lambda to find how the wavelength shifts in water, then apply Snell's law if the problem asks about angles, or simply track how the pulse behaves in each medium. Understanding that the bat's frequency stays constant while the wave "slows down" in denser water is what unlocks the physics here.

Intuitive explanation

This is a wave refraction problem where sound crosses from one medium to another. The key insight is that frequency never changes when a wave crosses a boundary—it's determined by the source—but wavelength and speed do. Use the wave equation v=fλv = f\lambda to find how the wavelength shifts in water, then apply Snell's law if the problem asks about angles, or simply track how the pulse behaves in each medium. Understanding that the bat's frequency stays constant while the wave "slows down" in denser water is what unlocks the physics here.

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