Question

While attempting to tune the note C at 131 Hz, a piano tuner hears 5.00 beats/s between a reference oscillator and the string.

(a) What are the possible frequencies of the string? (Give the frequencies to the nearest integer.)

lower possible frequency	Hz
higher possible frequency	Hz

(b) When she tightens the string slightly, she hears 6.00 beats/s. What is the frequency of the string now? (Give the frequency to the nearest integer.)
Hz

(c) By what percentage should the piano tuner now change the tension in the string to bring it into tune? (Give a positive answer for an increase in the tension, or a negative answer for a decrease in the tension.)
%

Answer 1

a] lower possible frequency = 131 - 5 = 126 Hz

higher possible frequency = 131+5 = 136 Hz

b] New frequency = 131+6 = 137 Hz

c] we know that, T2/T1 = (v2/v1)^2 = (f2/f1)^2 = (137/136)^2 = 1.01476 times

increase = (1.01476-1)*100 = 1.476 %