While tuning a string to the note C at 523 Hz, a piano tuner hears 2.00 beats/s between a reference oscillator and the string.

(a) What are the possible frequencies of the string?

(b) When she Bghtens the string, she hears 3.00 beats/s. What is the frequency of the string now?

(c) Assuming the string is now tuned to 526 Hz, by what percentage should she change the tension in the string to bring it into tune at 523 Hz?

a) the possible frequencies are 521hz, 522hz, 523, 524hz, 525hz

b) 526hz

c) 0.989 or a 1.14% decrease in tension

Explanation:

a) While tuning a string at 523 Hz, piano tuner hears 2.00 beats/s between a reference oscillator and the string.

The possible frequencies of the string can be calculated by

fl=f' - B

where

fl = lower limit of the possible frequency

f' = frequency of the string

B = beat heard by the tuner

fl = 523hz + Or - (2beats/secs * 1hz/1beat per sc)

fl = 521hz or 525hz

So the possible frequencies are 521hz, 522hz, 523, 524hz, 525hz

b) fl=f' - B

523hz = f' - 3

f' = 523 + 3 = 526hz

c) The tension is directly proportional to the square of the frequencies

T1/T2 = f1^2/f2^2

523^2 / 526^2 = 0.989 or a 1.14% decrease in tensio