Tension Calculation for a Vibrating Violin String

[bigsaucy]

A violinist places her finger so that the vibrating section of a 1.0g/m string has a length of 30cm, then she draws her bow across it. A listener nearby in a 20 degrees celsius room (speed of sound at this temperature in air is 343 m/s) hears a note with a wavelength of 40 cm. What is the tension in the string?


I was having real trouble with this question.

How are we meant to use the frequency of the wave in the air and transpose that information back into the string if we have no way of knowing the frequency/wavelength changes when the string hits the discontinuity of the medium (string-air)?

 

[Gregg]

You are usually given problems which you can do. Look at what you have here: \mu = 10^{-3} \text{kg/m} You are given the speed of sound in air, you are given the wavelength and you are asked to find the tension in the string.

How can you relate these quantities?

 

[bigsaucy]

Hello Greg.

I got the frequency in air to be 857.5 from the equation v = f lambda

Is the frequency of the sound wave in the air the same as the frequency in the string?
If yes, how is it that since some of the energy is transmitted to the the new medium (air in this case) and some transmitted back to the string, is the frequency the same?

 

[Gregg]

The frequency doesn't change. Do you have an equation for frequency of standing waves on a string?

 

[bigsaucy]

If i used f = 1/2L Sqrt (Tension/Linear Density) wouldn't I get the fundamental frequency? how are we meant to know if the frequency i calculated is the fundamental frequency?