A piano tuner who wishes to tune the note D2 corresponding to a frequency of 73.416 hertz has tuned A4 to a frequency of 440.000 hertz. Which harmonic of D2 (counting the fundamental as the first harmonic) will give the lowest number of beats per second, and approximately how many beats will this be when the two notes are tuned properly?
| Harmonic | Number of Beats | ||
| A. |
6
|
5
|
|
| B. |
6
|
0.5
|
|
| C. |
5
|
0.1
|
|
| D. |
3
|
0.372
|
|
| E. |
2
|
4.5
|
(GR9677 #81)
Solution:
Beats are the alternating constructive and destructive interference produced when two sound waves of different frequency approaching our ear. If there is no difference in frequency, there will be no beats. To minimize or to get the lowest number of beats, we set the beat frequency to zero.
440.000 − 73.416n = 0
n ≈ 440/73 ≈ 6
Number of beats = |440.000 − (73.416)(6)| = |440.000 − 440.496| = 0.496 ≈ 0.5
Answer: B
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