Can string diameter affect wave speed in guitar strings?

In summary: So the ratio of the wave speeds will be equal to the square root of the ratio of the tensions.In summary, the ratio of wave speeds, vA / vB, in two steel guitar strings with the same length can be found by using the equation v=square root of F/u, where u is the mass per length of the string. The ratio of the mass per length can be determined by finding the ratio of the volumes of equal lengths of the strings, which can be calculated using the formula 2pi*r^2*h. However, the 2pi and h will cancel out when calculating the ratio. Therefore, the overall equation for the ratio of wave speeds is equal to the square root of the ratio of the
  • #1
map7s
146
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Two steel guitar strings have the same length. String A has a diameter of 0.50 mm and is under 340.0 N of tension. String B has a diameter of 1.0 mm and is under a tension of 800.0 N. Find the ratio of the wave speeds, vA / vB, in these two strings.

I know that the equation that I need to use is v=square root of F/u where u=the mass per length of the string. I tried doing this solving by using that equation and just plugging in the diameters. Now that I've actually sat down and thought about it, I was wondering how I could incorporate the diameters into that equation, namely how can I figure out how to the diameter is related to the mass per length ?
 
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  • #2
The problem is assuming the strings are made of the same material, so they have the same mass per unit volume. A string with greater diameter has more volume, and hence more mass for a given length than a string with smaller diameter. Figure out the ratio of mass per unit length of the two strings by figuring out the ratio of the volumes of equal lengths of the strings
 
  • #3
So the volume would be 2pi*r^2*h but h would be the same for both equations and the 2pi would be constant and therefore cancel out when plugged into a ratio. So the overall equation would be something like v ratio=[square root of F/(r^2)] / same thing with the next set of numbers...right ?
 
  • #4
map7s said:
So the volume would be 2pi*r^2*h but h would be the same for both equations and the 2pi would be constant and therefore cancel out when plugged into a ratio. So the overall equation would be something like v ratio=[square root of F/(r^2)] / same thing with the next set of numbers...right ?
That's the right idea. Don't lose track of the constants, though they will divide out if you do a ratio.
 

What is the definition of wavelength on a string?

Wavelength on a string is the distance between two consecutive crests or troughs of a wave on a string.

How is wavelength on a string measured?

Wavelength on a string is measured by using a ruler or measuring tape to determine the distance between two consecutive crests or troughs of a wave on a string.

What factors affect the wavelength on a string?

The factors that affect the wavelength on a string include the tension in the string, the length of the string, and the speed of the wave traveling through the string.

What is the relationship between wavelength and frequency on a string?

There is an inverse relationship between wavelength and frequency on a string. As the wavelength increases, the frequency decreases and vice versa.

How does the wavelength on a string relate to the pitch of a sound produced?

The wavelength on a string is directly related to the pitch of a sound produced. A shorter wavelength results in a higher pitch, while a longer wavelength results in a lower pitch.

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