Natural Frequency and wavelength

[viciousp]

Homework Statement

The portion of a piano string between the bridge and upper end of the finger board is 0.50 meters long. The string when plucked sounds a note of 440Hz- the first harmonic.

a. where must the violinist put a finder to pay a C note- 528Hz
b Without returning, is it possible to play a D note- 294 Hz

Homework Equations

V(n)/2L=f

The Attempt at a Solution

a.
V(1)/(2)(.5)=440 Hz
V=440 m/s

528=440(1)/2L
L=.416, so the violinist must put his finger up .083 meters

b. 440(1)/2L=294
L=.748 meters, so no he can not.

Does my work make sense?

 

[Redbelly98]

Yes, looks good.