What is the Frequency of the Sound Wave Produced by a Vibrating Guitar String?

[Northbysouth]

Homework Statement

One of the 63.5-cm-long strings of an ordinary guitar is tuned to produce the note B3 (frequency 245 Hz) when vibrating in its fundamental mode.

A) Find the speed of transverse waves on this string.

B) If the tension in this string is increased by 1.0%, what will be the new fundamental frequency of the string?

C) If the speed of sound in the surrounding air is 344 m/s, find the frequency of the sound wave produced in the air by the vibration of the B3 string.

D) If the speed of sound in the surrounding air is 344 {\rm m/s}, find the wavelength of the sound wave produced in the air by the vibration of the B3 string.

Homework Equations

v = sqrt(T/μ) where T is tension and μ is the linear mass density which is equal to mass/length

fn = n*v/(2L) where n is the mode, v is the wave speed and l is the length

The Attempt at a Solution

I was able to solve parts A and B like so:

A) 2L*fn/n = v

thus

v = 2*0.635 m * 245Hz/1
v = 311.15 m/s

B)

I multiplied v by sqrt(1.01) thus v*sqrt(1.01) = 312.702

so

fn = (1*312.702 m/s)/(2*0.635m)
fn = 246.2 Hz

C) This is the part I'm stuck with. I tried:

fn = (1*344 m/s) / 2*0.635m)
fn = 270.9 Hz

My answer is wrong and I can't figure out how else to approach this problem. Could someone point me in the right direction?

D) I haven't tried to solve this part yet as I figured I probably need part C, or at the very least part C would help me solve it.

 

[Northbysouth]

Got it. Thanks.