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

Question

A piano tuners job is to make sure that all keys on nthe intrument 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 it first harmonic?

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

c) The proper freqeuncy for A is 440Hz. What tension would be required to obtain the proper frequency? Compare the necessary change in tension to the origianl value,by what fraction must the tension be changed?

Explanation / Answer

a) The first harmonic of the string f=1/2(T/ml)1/2 =0.5(2900/0.006(.63))1/2=0.5(.875899)(10)3 =.4379(10)3=437.9Hz =438Hz

b)the frequency can be changed by decreasing the length or linear density (for the same dimensions material of wire) and by increasing the tension in the string

c)already string has 438Hz frequency so to increase the frequency to 440Hz tension should be increased

here n is proportional to (T)1/2      so 438/440=(2900/T2)1/2   finally T2=2926.5 N

hence fractional change =26.5/2900=9.138(10)-3=0.0091

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