Frequency and Length: Solving for String Length

In summary, the conversation discusses the process of calculating the length of a string on a violin in order to produce a specific frequency of sound. The wavelength is determined to be twice the length of the string, and the velocity is found using the equation v = ƒλ. The length of the string can then be calculated using the velocity and desired frequency. It is noted that the part of the string that is vibrating is the section between the finger and the nut, and that the string can be played with a bow or by plucking. The final calculation involves subtracting the length of the string from the bridge to the finger (29.6 cm) from the length of the string from the finger to the nut (24.9 cm
  • #1
goonking
434
3

Homework Statement


upload_2015-9-23_20-54-40.png


Homework Equations

The Attempt at a Solution


for the first harmonic, the wavelength is twice the length of string.
so 0.296m x 2 = 0.592m is the wavelength

with the wavelength and frequency known, we solve for v in v = ƒλ

v = 0.592m x 440 Hz = 260 m/s

then to solve for the length of new string , we just use the same v (260 m/s) and use the new frequency (523 Hz) and solve for the L?

if so , I got 24.9 cm
 
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  • #2
goonking said:

Homework Statement


View attachment 89239

Homework Equations

The Attempt at a Solution


for the first harmonic, the wavelength is twice the length of string.
so 0.296m x 2 = 0.592m is the wavelength

with the wavelength and frequency known, we solve for v in v = ƒλ

v = 0.592m x 440 Hz = 260 m/s

then to solve for the length of new string , we just use the same v (260 m/s) and use the new frequency (523 Hz) and solve for the L?

if so , I got 24.9 cm
With regard to the parts of the string, what length have you calculated as 24.9cm? What length does it ask for?
 
  • #3
haruspex said:
With regard to the parts of the string, what length have you calculated as 24.9cm? What length does it ask for?
i calculated the length starting from beneath the finger to the nut to be 24.9 cm
 
  • #4
goonking said:
i calculated the length starting from beneath the finger to the nut to be 24.9 cm
What part of the string is vibrating at 523Hz?
 
  • #5
haruspex said:
What part of the string is vibrating at 523Hz?
just the 24.9 cm of string between the finger and nut I suppose since the rest isn't vibrating
 
  • #6
goonking said:
just the 24.9 cm of string between the finger and nut I suppose since the rest isn't vibrating
What is being used to make the string vibrate? What part of the string is it acting on?
 
  • #7
haruspex said:
What is being used to make the string vibrate? What part of the string is it acting on?
to make the string vibrate, you would have to pluck it, and if you held the string down with your thumb, only the part of the string between your thumb and the nut, will vibrate.
 
  • #8
goonking said:
to make the string vibrate, you would have to pluck it, and if you held the string down with your thumb, only the part of the string between your thumb and the nut, will vibrate.
You could do that, but you would get hardly any sound out of the violin. Whether played with a bow (as in the diagram) or plucked, it is the part between the bridge and the finger that is plucked or bowed. (The vibration is transferred through the bridge to the broad wooden lamina, and thence to the air inside.)
 
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  • #9
haruspex said:
You could do that, but you would get hardly any sound out of the violin. Whether played with a bow (as in the diagram) or plucked, it is the part between the bridge and the finger that is plucked or bowed. (The vibration is transferred through the bridge to the broad wooden lamina, and thence to the air inside.)
ah, I had to subtract the two, 29.6 cm - 24.9 cm = 4.7 cm.
 
  • #10
goonking said:
ah, I had to subtract the two, 29.6 cm - 24.9 cm = 4.7 cm.
Yes.
 

Related to Frequency and Length: Solving for String Length

1. What is the relationship between frequency and string length?

The frequency of a vibrating string is inversely proportional to its length. This means that as the length of the string increases, the frequency decreases and vice versa.

2. How is the string length determined in a vibrating string experiment?

The string length can be measured using a ruler or measuring tape. It is typically measured from the fixed end of the string to the point where it is attached to a movable object, such as a tuning peg or finger.

3. Why is it important to understand the relationship between frequency and string length?

Understanding this relationship is crucial in many scientific fields, such as acoustics and music. It allows us to calculate the frequency of a string and predict how changing the length of the string will affect its pitch.

4. How does the tension of a string affect its length and frequency?

The tension of a string is directly proportional to its frequency. This means that as the tension increases, the frequency also increases. However, the tension does not affect the length of the string.

5. Can the frequency of a string be changed without altering its length?

Yes, the frequency of a string can be changed by altering the tension. This can be done by tightening or loosening the string, which will affect its frequency without changing its length.

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