Determine the mass per unit length of the string.

In summary, the problem asks for the mass per unit length of a guitar's E-string, which has a length of 65 cm and is stretched to a tension of 85 N. The string vibrates at a fundamental frequency of 329.79 Hz. The formula for finding mass per unit length is tension divided by the product of frequency squared and twice the string length. After correcting for unit conversions and squaring the frequency, the mass per unit length is calculated to be 4.6e-4 kg/m.
  • #1
chess10771
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Homework Statement


A guitar's E-string has length 65 cm and is stretched to a tension of 85 N. It vibrates at a fundamental frequency of 329.79 Hz. Determine the mass per unit length of the string.
1Your answer is in kg/m


Homework Equations


(mass per unit length) = (tension) / ((frequency)x(wave length))^2


The Attempt at a Solution


The tension is 85 N, and the freq is 329.79 Hz, and how do i figure out the wave length, it thought the wavelength was twice the e string length in cm.
 
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  • #2
Yes, wavelength is twice the string length because the string is vibrating at its fundamental frequency.
 
  • #3
ok, i get an answe 1.5e-5 but its not correct am i doing something wrong
 
  • #4
I think you forgot to convert cm to m, and you didn't square the value for frequency. Using that formula you are supposed to get a value of 4.6e-4 kg/m, correct me if I'm wrong.
 

FAQ: Determine the mass per unit length of the string.

1. What does "mass per unit length" mean?

Mass per unit length refers to the amount of mass that is present in a given length of a string. It is typically measured in grams per meter (g/m) or kilograms per meter (kg/m).

2. How do you determine the mass per unit length of a string?

To determine the mass per unit length of a string, you will need to measure the mass of a known length of the string. Then, divide the mass by the length to get the mass per unit length. For more accurate results, it is recommended to take multiple measurements and calculate the average.

3. Why is determining the mass per unit length of a string important?

Knowing the mass per unit length of a string is important in various scientific and engineering applications. It can help in determining the strength and durability of the string, as well as its suitability for different purposes.

4. Can the mass per unit length of a string vary?

Yes, the mass per unit length of a string can vary depending on factors such as the type of material, thickness, and manufacturing process. It is important to measure the mass per unit length for each specific string being used.

5. Are there any units other than grams per meter or kilograms per meter for mass per unit length?

Yes, there are other units that can be used to measure mass per unit length, such as pounds per foot (lb/ft) or ounces per inch (oz/in). However, the metric units of grams per meter and kilograms per meter are more commonly used in scientific and engineering contexts.

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