Sound & Music, String Frequency

In summary, to find the frequency of the second mode of a string with a length of 0.50 m, a mass per unit length of 1.2 g/m, and a tension of 52 N, you can use the equation f = Vs/2L, where Vs = sqrt(F/μ). After correctly solving for Vs and taking the square root, the frequency of the second mode is found to be 416.33 Hz. It is important to consider significant figures when reporting results.
  • #1
Torrie
29
2

Homework Statement


Suppose a string is 0.50 m long, it has a mass per unit length of 1.2 g/m, and it is under a tension of 52 N. What is the frequency of the second mode of this string? Express your answer in the SI unit for frequency?

Homework Equations


f = Vs/2L Vs = sqrt (F/μ)

The Attempt at a Solution


I attempt to answer the second equation first to get Vs. Vs = sort (52 N/.0012 kg/m) And then plug 43333.33 into 43333.33/ 2(.50), and my answer is obviously wrong.
 
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  • #2
Torrie said:
I attempt to answer the second equation first to get Vs. Vs = sort (52 N/.0012 kg/m) And then plug 43333.33 into 43333.33/ 2(.50), and my answer is obviously wrong.

No doubt the "sort" was meant to be "sqrt". Did you forget to take the square root?
 
  • #3
It was meant to be sqrt. Thank you so much!
So the answer then is 208.17. Which means the frequency of the second mode is 416.33 Hz?
 
  • #4
Torrie said:
It was meant to be sqrt. Thank you so much!
So the answer then is 208.17. Which means the frequency of the second mode is 416.33 Hz?
Looks good!

You might want to be careful about specifying too many significant figures in any result you hand in. How many significant figures does your given data suggest that you use?
 

1. What is string frequency?

String frequency refers to the rate at which a string vibrates when it is plucked or struck. It is measured in Hertz (Hz) and determines the pitch of the resulting sound.

2. How does string frequency affect the sound produced?

The higher the frequency of a string, the higher the pitch of the sound produced. Lower frequencies result in lower pitches. This is because the frequency of a string is directly related to its wavelength, and shorter wavelengths produce higher pitches.

3. What factors affect string frequency?

The length, thickness, and tension of a string all affect its frequency. Longer strings vibrate at a lower frequency than shorter strings, and thicker strings vibrate at a lower frequency than thinner strings. Higher tension in a string results in a higher frequency.

4. How is string frequency used in musical instruments?

String frequency is used to create different pitches in stringed instruments such as guitars, violins, and pianos. By adjusting the length, thickness, and tension of strings, musicians can produce a wide range of frequencies and create a variety of musical notes and tones.

5. Can string frequency be altered?

Yes, string frequency can be altered by changing the length, thickness, or tension of the string. Additionally, by pressing down on different points along the string, musicians can change the effective length of the string and produce different frequencies. This is how different notes are played on instruments like guitars and violins.

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