How Does Beat Frequency Help Tune a Violin to Concert A?

[waterfolwer]

Homework Statement

A violinist is tuning her instrument to concert A (440 Hz). she plays the note while listening to an electronically generated tone of exactly that frequency and hears a beat frequency 3Hz, which increases to 4Hz when she tightens her violin string slightly. (a) what was the frequency of her violin when she heard the 3Hz beat? (b) to get her violin perfectly tuned to concert A, should she tighten or loosen her string from what it was when she heard the 3Hz beat?

Homework Equations

f beat= f1-f2

The Attempt at a Solution

F2= fbeat+f1 F2= 3Hz + 440Hz F2= 443Hz

The teacher has posted the solution to be 433Hz. Did he just make a typo, or am I doing something wrong?

 

[Dick]

Typo. Obvious typo.

 

[waterfolwer]

part b is confusing me. I would think that you would loosen the tension which would slow down the velocity which would reduce the frequency?

 

[Dick]

I would agree with you. Why would you doubt it? I think the key word here is 'slightly'.