Harmonics Question

[FIREitUP]

I've noticed a discrepancy in harmonics when it comes to standing waves with a node at one end and an antinode at the other. Some books say that there are no even numbered harmonics, and others don't mention this at all. So for instance, with nova physics it says the second harmonic: wavelength=3/4L
while in Kaplan, it says the third harmonic is that value, while stating that only odd numbered harmonics exist. can someone clear up the confusion for me, please?

---

Members don't see this ad.

 

[rprasan1985]

I've noticed a discrepancy in harmonics when it comes to standing waves with a node at one end and an antinode at the other. Some books say that there are no even numbered harmonics, and others don't mention this at all. So for instance, with nova physics it says the second harmonic: wavelength=3/4L
while in Kaplan, it says the third harmonic is that value, while stating that only odd numbered harmonics exist. can someone clear up the confusion for me, please?

You're right, there is discrepancy in the descriptions in different books. The idea conveyed is still the same- the harmonics in an open-ended system contain a node at one end and an antinode at the other. Also, for each harmonic the number of nodes equal the number of antinodes. The discrepancy seems to be in the naming convention. If we have an open-ended system and send waves through it, the first time a standing wave is generated is when wavelength = 4 L (n=1, so 'first' harmonic'). As we decrease the wavelength, the next time a standing wave is generated is when wavelength is 4/3 L (n=3, so 'third' harmonic). Notice that this is the second time a harmonic is observed. Some books refer to this as the 'second' harmonic. Others use the convention of naming the harmonic according to n, where n = 1, 3, 5 etc. EK refers to this as the third harmonic, and so does my college textbook. I'd say for the MCAT, go with third harmonic.

 

[FIREitUP]

You're right, there is discrepancy in the descriptions in different books. The idea conveyed is still the same- the harmonics in an open-ended system contain a node at one end and an antinode at the other. Also, for each harmonic the number of nodes equal the number of antinodes. The discrepancy seems to be in the naming convention. If we have an open-ended system and send waves through it, the first time a standing wave is generated is when wavelength = 4 L (n=1, so 'first' harmonic'). As we decrease the wavelength, the next time a standing wave is generated is when wavelength is 4/3 L (n=3, so 'third' harmonic). Notice that this is the second time a harmonic is observed. Some books refer to this as the 'second' harmonic. Others use the convention of naming the harmonic according to n, where n = 1, 3, 5 etc. EK refers to this as the third harmonic, and so does my college textbook. I'd say for the MCAT, go with third harmonic.

Cool, thanks. I guess I'll just use the EK equation.