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enter image description hereI am a physics teacher and I was discussing interference patterns related to tuning forks with a colleague. She demonstrated the interference, which was very obvious. As she rotated the tuning fork, the volume of the tone increased and decreased dramatically. She showed me this diagram as a reference when explaining the phenomenon.

This explanation does not make sense to me for two reasons: 1) Assuming that the diagram referenced is correct, I do not understand how any point in space could be a half-wavelength further from one tine than the other when the tines are only 0.02m apart and the wavelength produced is approximately 1.3m. 2) The diagram referenced shows areas of compression leaving each tine simultaneously and traveling outwards in concentric circles. That does not seem likely to me. If the tines are vibrating back and forth, it seems that whenever an area of compression left one side of the tine, an area of rarefaction should leave the other side of the tine.

Am I thinking about this incorrectly? Any explanations?

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Tuning forks are more complicated than the simple picture you posted. Because there are two tines, they will emit sound more like quadrapoles (i.e, with a kind of clover-leaf loudness pattern) than as two independent sources of spherical waves. So the answer to your first point is no, the diagram is not entirely correct - as you rotate the tuning fork, the sound will get louder then dimmer a total of four times independent of any conventional interference effects.

As to your second questions, the fundamental vibration mode is when the tines vibrate out of phase (one goes left as the other goes right). Moving left-right together is possible but that vibration has a higher pitch. So your picture is correct in that sense at least.

There's a nice page on tuning forks (with animations of different tuning fork motions) at Penn State

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    $\begingroup$ Thank you for your response and the link to Penn State. I found my way to this page (acs.psu.edu/drussell/demos/rad2/mdq.html) whose animation helped me understand what was happening. Thanks again! $\endgroup$ – Dan Apr 16 '18 at 18:24
  • $\begingroup$ Minor comment: the in-phase mode is not only a different pitch but also gets damped much more rapidly, because it transfers energy to the handle and then to your hand, which absorbs it. This is deliberate - they have two prongs in order to ensure that a single mode dominates. See my answer to physics.stackexchange.com/questions/51847/… $\endgroup$ – Nathaniel Apr 17 '18 at 1:59
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Your wavelength problem makes sense. I pulled out my tuning fork (128 Hz Sklar)--it has deep nodes. I think it's because the radiation isn't isotropic, rather it has a quadrupole pattern, and that is the source of the nodes.

I count 4 as I go around it. I think they are so noticeable because it's a high-Q oscillator.

If you have more than one frequency (of the same model), and the nodes are in the same spots: you can rule out interference.

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The tuning fork acts as a pair of stiff rods with boundary conditions. In fact you can match the harmonics to formulae found in Fletcher and Rossing. As for the pattern in space, this is a directional device. The same type of directionality results from a phased array. As for your comment about not being exactly a half wavelength out of phase... was the amplitude exactly zero? I think your second statement is not universally true. Whether the tines are in phase or out of phase w/r to the compression or rarefaction would depend on from which direction you are viewing the tuning fork. (I am not sure if you are referring to this phenomena coming from opposite sides of the same part of the fork or from two different tines.)

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