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

Question

A piano tuners job is to make sure that all keys on the instrument produce the proper tones. On one piano, the string for the middle A-key is under a tension of 2900 N. It has a mass of 6.000 g and a length of 63.00cm

a.)What is the current frequency if the string is excited in its first harmonic?

b.)How can the frequency be changed? Give at least 2 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?

Please answer each part with detailed steps so that I understand what it takes to do the problem properly. Thank you in advance!

Explanation / Answer

Here ,

Tension , T = 2900 N

mass , m = 0.006 Kg

L = 0.63 m

a)

frequency = sqrt(T*L/m)/(2L)

frequency = sqrt(2900 * 0.63/.006)/(2 * 0.63)

solving

frequency = 437.95 Hz

the fundamental frequency is 437.95 Hz

b)

the frequency can be changed by chnaging the tension and by changing the length of string

c)

let the tension is T

frequency = sqrt(T*L/m)/(2L)

440 = sqrt(T* 0.63/.006)/(2 * 0.63)

solving for T

T = 2927 N

the new tension in the string is 2927 N

fraction of change in tension = (2927 - 2900)/2900

the fraction of change in tension is 0.0093

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.