The frequency of a wave comes from the rate at which the disturbance at the source takes place. My question is, what parameters (on the guitar for example) determine that one string delivers a low pitch sound and that another delivers a high pitch (thus, frequency) one? And if for example, i am hitting a table with the same intensity, but with different frequencies, say one time with 1hit/second and the other time with 5hits/second, should i notice a different of pitch?
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$\begingroup$ These links might be helpful: physics.stackexchange.com/questions/269628/… and physics.stackexchange.com/questions/31071/physics-of-a-guitar $\endgroup$– alfredCommented Dec 28, 2019 at 15:41
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2$\begingroup$ Does this answer your question? Music / Harmonics $\endgroup$– NotMeCommented Dec 28, 2019 at 15:41
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2 Answers
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The velocity of propagation of a wave in a string ( v ) is proportional to the square root of the force of tension of the string ( T ) and inversely proportional to the square root of the linear density ( $\mu$ ) of the string:
$$ v=(T/\mu)^{1/2} $$
Once the velocity of propagation is known the fundamental harmonic frequency is given by:
$$ f=(v/(2L))=(1/(2L))(T/\mu)^{1/2} $$
where T is the tension, $\mu$ is the linear density (that is, the mass per unit length), and L is the length of the string.
You can see that the frequency is not a function of the plucking force amplitude. It is a function of the tension, the length, and the linear mass density.
answered Dec 28, 2019 at 18:07
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This is a complex question. The pure vibration of a string at a single frequency takes on a sine wave pattern. The plucking of a string deforms the string in a non-sine shape, so the disturbance is a linear combination of sine and cosine (a $\pi/2$ phase shift of sine) of multiple frequencies which are determined by properties of the string. The string acts as a filter for the plucking so the string only vibrates with certain frequencies. The sound wave produced in the air will correspond to the frequencies of the wave on the string.
On the other hand, consider a loudspeaker to which an electrical sine wave voltage is applied. The speaker will push and pull at the frequency of the voltage, causing pressure compressions and rarefactions in the air, independent of the size and material of the speaker.
When striking a table (or drum), each strike will be similar to the pluck of the string: the table or drum will filter the frequency content of the strike (actually a continuum of frequencies, initially) to the basic resonant frequencies. BUT as the rate of striking increases, two things could happen: 1) the rate of striking could reach the audible range, and 2) on a drum, the strike rate may be fast enough to change the average tension in the drum head causing a general rise in the resonant frequencies. This often happens in tympani and tabla.
