How do you determine the wavelength of the string?

In summary, the string is 1m in length, has a mass of 100g, and a tension of 10N. To determine the wavelength, the wave velocity must be calculated using the square root of the tension over the linear density. This can then be used to find the wavelength by dividing 1 by the frequency of 9.5 Hz. However, there was a mistake in the calculation of the wave velocity, as the tension was meant to be 1N instead of 10N.
  • #1
~angel~
150
0
There is a string 1m in length, 100g in mass and has tension of 10N. 9.5 Hz of frequency is applied to it.

I know this question is meant to be simple but how do you determine the wavelength of the string?

Thank you.
 
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  • #2
The wave velocity is given by the square root of (tension over linear density).
Once you know the wave velocity you can get the wave length from that and the frequency.
 
  • #3
The wavelength is one over the frequency, so just divide 1 by 9.5 and that tells you the lenghth of one period or the wavelength.
 
  • #4
HallsofIvy said:
The wave velocity is given by the square root of (tension over linear density).
Once you know the wave velocity you can get the wave length from that and the frequency.

The linear density has units of kg/m, right? So v = 10/0.1^(1/2) = 10m/s. But when this is substituted into v=wavelength*f, the wavelength is 1.05, which doesn't make sense.
 
  • #5
Ok velocity of wave in a string with tension is given by:

[itex]

v= \sqrt \frac{T}{m}

[/itex]


where m=mass per unit length.


Now apply v=f(Wavelength) to get the answer
 
  • #6
I misread the tension (it was meant to be 1N).

Thanks guys.
 

1. What is the formula for determining the wavelength of a string?

The formula is: wavelength = 2 x length of string x sin (angle of vibration)

2. How do you measure the length of the string?

The length of the string can be measured using a ruler or a measuring tape.

3. What is the angle of vibration and how do you measure it?

The angle of vibration is the angle at which the string vibrates. It can be measured using a protractor.

4. Can the wavelength of a string change?

Yes, the wavelength of a string can change depending on the tension, length, and density of the string. It can also be affected by external factors such as temperature and humidity.

5. How does the wavelength of a string affect its pitch?

The shorter the wavelength, the higher the pitch will be. This means that as the string vibrates with a shorter wavelength, it produces a higher frequency of sound, resulting in a higher pitch.

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