Wave speed, freq, and period of wave on a string

AI Thread Summary
The discussion centers on calculating the wave speed, frequency, and period of a vibrating guitar string after specific finger placements. The initial calculations for wave speed, frequency, and period were performed using the tension and linear mass density of the string. However, there was confusion regarding the correct wavelength after the fingers were removed, as the user mistakenly used the distance from the fret to the origin instead of the entire length of the string. Clarification was needed on how to incorporate the full length of the string into the calculations. The thread highlights the importance of accurately determining the wavelength to obtain the correct frequency and period.
dinospamoni
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Homework Statement



A musician frets a guitar string of length 1.5 m at x = 0.34 m with one finger, and simultaneously plucks the string at x = 0.17 m with another finger (raising it to a height h = 2.1 mm. Both fingers are simultaneously removed from the string, and it is allowed to vibrate. The string has a tension of 76 N, and a linear mass m = 4.9 g/m.

Homework Equations



v=\sqrt{\frac{T}{\mu}}
where
\mu=\frac{mass\,in\,kg}{Length\,in\,m}

v=f\lambda



The Attempt at a Solution



I started off converting the linear mass:

4.9\frac{g}{m} \times\frac{1 kg}{1000 g} = .0049\frac{kg}{m}

Then I plugged that into the equation:

v=\sqrt{\frac{76 N}{.0049\frac{kg}{m}}}

and got v=124.54 m/s

From here I used v=f\lambda
where \lambda=.68 m

and got frequency = 183.147 Hz

Taking the reciprocal of that:

Period = .00546 s

These aren't the right answers, but I don't see where I went wrong

Also, picture attached
 

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You don't say exactly what is being asked. You have calculated, correctly I believe, the period as though the fret finger is still in place, but is it what was asked for?
 
I included what was asked for in the title, but forgot to include it in the question. It's asking for the wave velocity, frequency, and period.

I accounted for the finger being lifted off by making the wavelength twice the interval between the finger and the origin. Is that not right?
 
dinospamoni said:
I included what was asked for in the title, but forgot to include it in the question. It's asking for the wave velocity, frequency, and period.

I accounted for the finger being lifted off by making the wavelength twice the interval between the finger and the origin. Is that not right?
No, that's what it would be if the finger were left in place. But even then, 1.5m is not twice 0.34m. How do you propose to bring 1.5m into the equation?
 
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