# Homework Help: Highest harmonic of a string within typical human's audible range

1. Sep 26, 2008

### hemetite

1. The problem statement, all variables and given/known data

What is the highest harmonic of this string that is within the typical human's audible range (up to 20000 Hz)

String length of 16m
u = liner density = 0.015 g/cm = 0.0015 kg/m
stretched tension of the string = 557N

2. Relevant equations

v= sqrt ( F/ u)

v= lamba * frequency

lamba = 2 Length / n

3. The attempt at a solution

v= sqrt ( F/ u) = sqrt ( 557/0.0015 ) = 609.37

up to human's typical audible frequency = 20000 Hz

v= lamba * frequency
609.37 = lamba * 20 000 Hz
lamba = 0.0304685

therefore lamba = 2 length /n

0.0304685 = (2* 16) / n

n=1050.265

Ans: the highest harmonic of the string that is within human's audible range = 1050 harmonics.

Am i right?...

2. Sep 26, 2008

### Redbelly98

Staff Emeritus
Yes, well done.

3. Sep 26, 2008

### hemetite

thaank...u.... :)

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