The speed of waves on a string is 97 m/s. If the frequency of standing waves is 475 Hz, how far apart are two adjacent nodes?
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This is Giancoli Answers with Mr. Dychko. Adjacent nodes and a waveform are half a wavelength apart. So, from this node to this node is one full wavelength because the wave is, you know, identical of these two points in the sense that it's going, the slope is upwards to the right and upwards to the right as well as having zero displacement. Whereas this point slope is down to the right and so it's not the same as this point, it's not congruent. So, the wavelength goes from one node not to the next node but to the one after that. So, the distance between adjacent nodes then is half the wavelength. And we have this formula that says that the speed of a wave is this frequency times this wavelength. And we can divide both sides by f. And that gives wavelength is v over f and then knowing that this distance, l, we're looking for between, distance between adjacent nodes is wavelength over 2 we have 1/2 times v over f. So it's 1/2 times 97 meters per second divided by 475 hertz which is 0.10 meters.
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