In: Physics
While attempting to tune the note C at 2093 Hz, a piano tuner hears 6.00 beats/s between a reference oscillator and the string.
(a) What are the possible frequencies of the string?Lower possible frequency=2087 Hz/ Higher possible
frequency=2099 Hz
(b) When she tightens the string slightly, she hears 7.00 beats/s.
What is the frequency of the string now? 2100
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.)
a )
we have equation is using here is
number of beats = frequency of oscillator frequency of piano wire
6 = 2093 fp
fp = 2093 6
= 2099 Hz or 2087 Hz
Lower possible frequency=2087 Hz
and
Higher possible frequency=2099 Hz
b )
the frequency of the string now is
fp ' = 7 + fo
= 7 + 2093
= 2100 Hz
the frequency of the string now is = 2100 Hz
c )
f = k T
2093 = k To
To = 20932 / k2
T1 = 21002 / k2
T % = ( ( T0 - T1 ) / T1 ) x 100
= ( ( 20932 - 2100 ) / 2100 ) x 100
T % = - 0.6655 ( decrease in the tension )