How to Calculate Wave Velocity in a Tuned Violin String

[Daltohn]

Homework Statement

A tuned violin, with strings of 31.6 cm each, is placed in front of a speaker. When varying the speakers frequency between 500 and 1500 Hz, it was discovered that a certain string only vibrated at 880 Hz and 1320 Hz. Determine the velocity of the wave in this string.

Homework Equations

v=fλ

The Attempt at a Solution

The frequencies has to be overtones or the fundamental tone f_0. That gives nf_0=880 Hz and (n+1)f_0=1320 Hz, so n=2 and f_0=440 Hz. When f=f_0 the string has two nodes so v=f_0*2l (l=0.316m). v=278.08. But the key says 275 m/s, did I do something wrong or have they rounded it weirdly? Thanks

 

[Adithyan]

I don't see anything wrong in your solution. It most probably is a case of rounding off weirdly.

 

[Daltohn]

I don't see anything wrong in your solution. It most probably is a case of rounding off weirdly.

Yes, has to be so. Thanks :)