Length on vibrating section of violin

[chicagobears34]

Homework Statement

A particularly beautiful note reaching your ear from a rare Stradivarius violin has a wavelength of 39.1 cm. The room is slightly warm, so the speed of sound is 344 m/s.

If the string's linear density is 0.560g/m and the tension is 160N , how long is the vibrating section of the violin string?

Homework Equations

f=c/wavelength
f=sqrt(F/(m/L))/(2L)

The Attempt at a Solution

frequency = (344m/s) /(.391m) = 879Hz
879=sqrt(160/(.000560/L))/(2L)
i converted .560g/m to .000560kg/m because force is in Newtons
did algebra and got that length is 10.81m, which is wrong.
Not sure what I did wrong though.

 

[haruspex]

879=sqrt(160/(.000560/L))/(2L)
i converted .560g/m to .000560kg/m because force is in Newtons
did algebra and got that length is 10.81m, which is wrong.
Not sure what I did wrong though.

Looks like an arithmetic error. Can't tell what you did wrong if you don't post all your work.

 

[gneill]

You were given the linear density of the string, not its entire mass. So no need to divide it by L in your velocity expression.

 

[chicagobears34]

yes i was given the linear density, so I shouldn't have done m/L
that's what I what was doing wrong.
Thanks

 

[haruspex]

yes i was given the linear density, so I shouldn't have done m/L
that's what I what was doing wrong.
Thanks

Rats - I noticed that but dismissed it as a typo.