I recognize that for a string of linear density \$mu\$ and also tension \$T\$, the wave rate is provided by \$v=sqrtfracTmu \$.

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Additionally, the rate of any type of sinusoidal wave is offered by \$v=lambda f\$.

My inquiry is: execute both the frequency and the physical properties that the string identify the wave speed or simply one that these?

Those 2 equations call you

1) The rate of a wave on a string relies on only tension and also density of the medium, no the frequency that the source.

2) IF the frequency the the resource if \$f\$, girlfriend can find the wavelength by \$lambda = v/f\$. High frequency resources produce much shorter wavelengths, and vice versa. You"re NOT cost-free to choose both the wavelength and the freqency; if the frequency that your source is \$f\$, it will necessarily have wavelength \$lambda =v/f\$.

All the waves have actually the exact same speed, provided by \$sqrtfracTmu\$. The 2nd equation is basically informing you the on this string, you can"t produce a tide with any kind of frequency and wavelength. You can only create waves satisfying \$lambda f = v\$.

Trust the math. The an initial equation provides a specific speed of the wave. 2nd equation gives a relation between speed, frequency and also wavelength. You don"t gain much details out of second equation yet the first equation explicitly states the the velocity depends upon the medium. Just take sound for example, if the speed were dependency on frequency the moment interval in between hearing of 2 notes would certainly be heavily dependent upon their respective frequencies. This would certainly make music an extremely messy yet in real life it is not.

Most an easy waves the you"ve studied more than likely obey the tide equation: https://en.wikipedia.org/wiki/Wave_equation#Scalar_wave_equation_in_one_space_dimension. This equation describes countless kinds the commonly-encountered waves rather well: e.g. Vibrating guitar strings, water ripples, sound waves v air, light traveling though north space. These kinds of tide are figured out entirely by the tool through i beg your pardon they travel (e.g. The thickness of the air or the thickness the the etc string).

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But waves traveling v more complex materials have the right to experience a phenomenon called dispersion and are no longer explained by the an easy wave equation. Approximately speaking, a dispersive wave"s speed relies on that is frequency, and therefore top top the frequency that its source. Much more technically, it"s actually not noticeable how to even define the "speed" the a dispersive wave. One have the right to talk about the "phase velocity," which (roughly) method the speed at which tiny ripples move, or the "group velocity," which (roughly) means the rate at i beg your pardon a huge envelope containing many smaller ripples moves. The easiest means to gain an intuition top top the distinction is probably simply to search "group and phase velocity" top top YouTube and also look at some video clip clips.