Tension In a string Second Harmonic

• Punkyc7
In summary, the string must be tensioned at a very high frequency in order to produce a wavelenght of 3.39 cm.
Punkyc7
One string of a certian musical intrument is 79 cm long and it has a mass of 8.74 g. It is being played in a room where the speed of sound is 344m/s
To what tension must you adjust the string so that when vibrating in its second overtone it produces a wavelenght of 3.39 cm

v=sqrt(T/mu)
f=nv/2l
v=lambda f

f=344/.0339=10147.49 hertz

10147.49=v/l=sqrt(T/m/l)/l

which gives me a tension of 710977.38 N which seems to large for a string on an instrument. Is that right?

Last edited:
It is correct. Remember, the tension is force/m2 and the diameter of a string is in the mm range. Multiplying the tension with the cross section area of the string results in a small force.

ehild

ehild said:
Multiplying the tension with the cross section area of the string results in a small force.

ehild

But isn't the force really big?

Yes, you are right, it is a very big force, I was mistaken. Are you sure that the data are correct?

ehild

thats what i was given but it seems to large to be reasonable

I think the frequency is very high, that is why the tension is so impossibly great.

ehild

Last edited:
So you can't use the speed of sound as v in this problem?

how about a f of 435.44 does that sound more reasonable

that gives me 19698 N which still seems to high

Last edited:
Your solution was correct. The force corresponds to the numerical data given. The given wavelength in air corresponds to a very high frequency.
The mass is also too high. If the string is made of steel, the diameter can be of 1.3 mm.
In case of a guitar string, for example, a typical diameter is of 0.5 mm and the tension of 100 N. But the mass would be about 1 g then.

ehild

1. What is tension in a string second harmonic?

Tension in a string second harmonic refers to the amount of force or stress applied to a string in order to produce a standing wave with the second harmonic. This tension is necessary for the string to vibrate at the desired frequency and produce the desired sound.

2. How is tension in a string second harmonic measured?

Tension in a string second harmonic is typically measured in units of newtons (N) or pounds (lbs). This can be done using a tension meter or by calculating the tension based on the properties of the string, such as its length, mass, and material.

3. What factors affect tension in a string second harmonic?

The tension in a string second harmonic can be affected by various factors, including the length and thickness of the string, the material it is made of, and the amount of force applied to it. Tension can also be affected by external factors such as temperature and humidity.

4. Why is tension in a string second harmonic important?

Tension in a string second harmonic is important because it determines the frequency at which the string will vibrate and produce sound. Different amounts of tension can result in different pitches, and adjusting the tension can also affect the quality and clarity of the sound produced.

5. How is tension in a string second harmonic used in scientific research?

Tension in a string second harmonic is used in scientific research to study the properties of sound and how it is produced. By manipulating the tension in a string, scientists can observe how it affects the frequency and quality of the sound produced, and use this information to better understand the physics of sound and vibration.

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