A piano tuners job is to make sure that all keys on the piano produce the proper

Question

A piano tuners job is to make sure that all keys on the piano produce the proper tones, On one piano, the string for the middle A-key is under a tension of 2900N. It has a mass of 6.000g and a length of 63 cm . A) What is the current frequency if the string is excited in its first harmonic? B) How can the frequency be changed? Give atleast two options C) The proper frequency for A is 440 Hz. What tension would be required to obtain the proper frequency? Compare the necessary change in tension to the original value, i.e. by what fraction must the tension be changed?

Explanation / Answer

part A: frequency of string f = nv/2L

speed v^2 = T/u

where T is tension u is mass per unit length

so

V^2 = 2900/(6 e -3/0.63)

V = 551.8 m/s

so f = (1 * 551.81/(2* 0.63)

f = 438 Hz

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f = nV/2L = (1/2l) sqrt(T/u)

f can be changed by changing Tension in the sting a

and mass attached to it

---------------------------------------------------------------------

for f = 440 Hz

sqrt(T/u) = 2Lf = 2* 0.63 * 440

T/u = 554.4^2 = 307359.36

T = 307359.36 * 6 e -3/0.63

T = 2927.23 Hz (ANSWER)

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