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A guitar string with a linear density of 2.0 g/m is stretched between supports that are...

A guitar string with a linear density of 2.0 g/m is stretched between supports that are 60 cm apart. The string is observed to form a standing wave with three antinodes when driven at a frequency of 420 Hz. What are (a) the frequency of the fifth harmonic of this string and (b) the tension in the string?

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Answer #1

a)

fn=nth harmonic frequency=nf1   (1)

f1= fundamental frequency

3 antinode means 3rd harmonic f3=420Hz (given) and f5=?

from eqaution (1)

f5=700Hz

b)

using (1) f1=fn/n=f3/3=140Hz

v=velocilty of wave=2Lf1=2x60cmx140Hz=168m/s

L= length of string

T=tension on string

=linear mass density of the string

So Tension on the string T=56.448N

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