Highest harmonic of a string within typical human's audible range

AI Thread Summary
The discussion focuses on calculating the highest harmonic of a 16-meter string within the human audible range of up to 20,000 Hz. Using the formula for wave speed, the velocity is determined to be 609.37 m/s based on the string's tension and linear density. The wavelength corresponding to the maximum frequency is calculated as 0.0304685 m. By applying the relationship between wavelength and harmonic number, it is concluded that the highest harmonic is approximately 1050. The solution is confirmed as correct by other participants in the discussion.
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Homework Statement



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

Homework Equations



v= sqrt ( F/ u)

v= lamba * frequency

lamba = 2 Length / n


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?...
 
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