wave speed question, please help :)

Question

On a stringed instrument, the n=3 harmonic gives a frequency of 419 Hz. The length of the string is 0.48 meters. Find the wave-speed on this string. 
in terms of meters/second. 
to a precision of tenths of a m/s. Use a format like ##.# or ###.# in your answer.
to an accuracy of 0.2 m/s. 

Answer 1

Fundamental is First harmonic ( n =1)

Second harmonic = 2x Fundamental frequency  ( n= 2)

Third harmonic = 3x fundamental ( n=3 )

 

Given 3f = 419 

f = 419/3

L= 0.48 m. This length will have three loops 

Length of one loop = 0.48 / 3 = 0.16 m = Wave length /2

So wave length = 0.32 m

Using  Wave speed = frequency x Wave length

 

Wave speed = (419/3)x (0.32) m/s = 44.69 m/s

 

for accuracy 0.2 m/s

Speed = 44.7 m/s