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Kay [80]
3 years ago
8

Piano tuners tune pianos by listening to the beats between the harmonics of two different strings. When properly tuned, the note

A should have the frequency 440 Hz and the note E should be at 659 Hz . The tuner can determine this by listening to the beats between the third harmonic of the A and the second harmonic of the E.
A tuner first tunes the A string very precisely by matching it to a 440 Hz tuning fork. She then strikes the A and E strings simultaneously and listens for beats between the harmonics. The beat frequency that indicates that the E string is properly tuned is 2.0 Hz
The tuner starts with the tension in the E string a little low, then tightens it. What is the frequency of the E string when she hears four beats per second?
Physics
1 answer:
mote1985 [20]3 years ago
5 0

Answer:

Frequency = 658 Hz

Explanation:

The third harmonics of A is,

f_{A}=(3)(440Hz)=1320Hz

The second harmonics of E is,

f_{E}=(2)(659Hz)=1318Hz

The difference in the two frequencies is,

delta_f = 1320 Hz - 1318 Hz = 2 Hz

The beat frequency between the third harmonic of A and the second harmonic of E is,

delta_f = 3f_{A}-2f_{E}

f_{E}=\frac{3f_{A}-delta_f}{2}

We have calculate the frequency of the E string when she hears four beats per second, then

delat_f = 4 Hz

f_{E}=\frac{3(440Hz)-4Hz}{2}

f_{E}=658Hz

Hope this helps!

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