Question

Dolphins make sounds in air and water. What is the ratio of the wavelength of a sound in air to its wavelength in seawater? Assume air temperature is $20.0^\circ\textrm{C}$.

Final Answer

$0.223$

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Video Transcript

This is College Physics Answers with Shaun Dychko.
We're going to find the ratio of wavelengths of this particular frequency that a dolphin makes, if that sound is travelling through the air versus travelling in salt water. I have subscripts

*sw*here to denote salt water. Now the wave speed in air is going to be the frequency multiplied by the wavelength in the air and the speed of this sound in saltwater is going to be the same frequency multiplied by the wavelength in saltwater. So notice that the frequency does not have a subscript because the frequency is not changed by the medium. When the sound goes through the different medium, so water versus air, the frequency will be the same. It is just the wavelength that will change as well as a corresponding change in the speed of the wave of the sound. So, we can divide this by this here and the frequencies will cancel giving us the ratio of the wavelength in the air to that in the saltwater. And that is also equal to the speed of the wave and air divided by the speed of the wave and water. So the textbook and the version of the pdf I have on page 737, the speed of sound in air is 343 meters per second. And if you look at table 17.4, the speed of sound in salt water 1540 meters per second and this gives a ratio of 0.223. So the wavelength in the air is going to be a lot less than the wavelength in salt water.