When you slosh the water back and forth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 75-cm-wide tub is 0.85 Hz. What is the speed of the water wave?
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This is Giancoli Answers with Mr. Dychko. Here's a picture of the wave at one moment and then some time later, we have the way of looking like this. So, we have the water at a high point at this end of the tub on one hand and a low point at the other end of the tub. And then sometime later this end of the tub gets the high point and this end gets the low point with the middle staying relatively calm. So, there's a node in the middle and antinodes at each end. And this is half of a wavelength because a full wavelength would go all the way here like this. And... So what I've drawn here with including the dotted line is a full wavelength, and this would make half of it. So, the tub length is half a wavelength and so the wavelength is 2 times length of the tub and that's 2 times 75 times 10 to the minus 2 meters and that's 1.5 meters. And so the wave speed is frequency times wavelength 0.85 hertz times 1.5 meters which is 1.3 meters per second.
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