The lowest note on a grand piano has a frequency of 28.1 Hz. It is a fixed string oscillating in its fundamental (longest wavelength) mode. The string is 2.00 m long and has a mass of 340 g. What tension is needed to tune this string properly to the frequency of 28.1 Hz

Question

Physics

Johan Lucero

19 February, 20:56

The lowest note on a grand piano has a frequency of 28.1 Hz. It is a fixed string oscillating in its fundamental (longest wavelength) mode. The string is 2.00 m long and has a mass of 340 g. What tension is needed to tune this string properly to the frequency of 28.1 Hz

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Answers (1)

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Emerson Gutierrez · Answer 1

2210.91 N

Explanation:

f = v/∧ = 1/2 √ T / μ

where f = 28.1 Hz, T = tension,

L = 2m

mass density = μ = 350:1000/2.00

= 0.175kg/m

from f = 1/2L √ T / μ

make T the subject of the formula

T = (f*2L) ² ₓ μ

T = (28.1*2*2) ² * 0.175

T=12633.76*0.175

=2210.91 N