At the level of instrument tuning accuracy that effect will not be bad enough to cause unacceptable pitch accuracy, since it is well below about 0.1 Hz or 1 cent in the forks I have studied music sounds OK within that accuracy. That effect is called "overdrive" or running an oscillator in the "non-linear regime" but of course that effect is always present to some degree, if you look close enough, in any parameter regime. Those onomatopoeias mimic the characteristic frequency rise as the oscillator's sound quickly dies out, the metal swings through smaller and smaller arcs and so the restoring force of the metal becomes more and more linear versus displacement distance. Thus cheap soft metal oscillating things go "boing" or "twang". The tines have farther to move and though the internal restoring force also increases with displacement, it will not be enough to exactly keep the frequency steady. If the tines of a tuning fork are struck very hard the frequency will be lower because All physical harmonic oscillators will change their frequency versus the amplitude of oscillation, (even precision pendulum clocks). However it must of course be there at some level. But so far I know the pitch change with (normal) amplitudes is below 0.1Hz and below 1 cent. I could start it ringing with an electromagnet oscillating at the fork's frequency, but haven't done that yet, afraid it will be hard to get large enough amplitudes. If I hang it from a string then it swings from the striking to start its oscillation. If the fork is held in a vice to end doppler effects then it dies out too quickly. I've searched for the frequency shift versus amplitude of 261Hz to 523Hz forks in the milliHertz range, but it is very difficult to measure because competing effects at that level: even doppler effects from the motion of my hand holding the fork in front of the microphone creates frequency shifts of a few centiHertz, and energy of the moving tines converts into heat in the metal which could change the frequency, any temperature gradient in the room pulls the pitch at the level of 1000ppm per 10 degrees Fahrenheit. Now I will explore that result with the much less useful philosophy technique appropriate to this website: On a graph from my experiment on a hand held fork I measured in 2015 I showed that over the ~minute the fork was oscillating the pitched dropped approximately linearly from 524.091Hz to 524.082Hz, end of factual information. This website does not allow me to post evidence like data files or graphs or sound files, so you will have to do it on your own if you want to see. That will give accuracy to around 0.01Hz. Measurements on the topic for this forum can be done by holding a $8 tuning fork in front of a mic, then analyze the sound file with the free program "SpectraLabs" using the "Waterfall" display and using the built in Goertzel frequency extraction algorithm. You can start a pendulum swinging, count time with it, and as the swings slowly diminish they will keep marking the same time intervals. For small amplitudes of oscillation, its frequency is independent of the amplitude. Objects tend have “natural” frequencies at which they oscillate, determined by intrinsic properties like their mass and their restoring forces.Īnother example is a pendulum (which is like a swingset). You can push your child gently or forcefully in the swing, but the swing “wants” to swing at a frequency determined by its length and the strength of Earth’s gravity. The approximation is good for weak strikes if you strike it really hard, the approximation becomes worse and it can affect the frequency, so be gentle with your tuning fork. To a first approximation, a tuning fork’s frequency is determined by its mass, stiffness, and shape, which are fixed. Does the frequency of a tuning fork depend on the strength by which it is struck?
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