If you place your hand on a piano and play a note, you will feel the piano vibrate. The number of vibrations per second (hertz) of a note is called its frequency. If you strike the piano keys from left to right, the frequencies of the notes increase. We use combinations of letters of the alphabet, numbers, and sometimes the €œsharp€ symbol # to refer to these notes (see Fig. 39). The frequencies of 13 notes in a row are listed in Table 38.
Fig. 39

Let y be the frequency (in hertz) of the note that is x notes above the note A3.
a. Construct a scatterplot.
b. Find an equation of a model and graph it on the scatterplot. Then describe the shape and the strength of the association.
c. What is the y-intercept? What does it mean in this situation?
d. Use the model to predict the frequencies of the notes E4 and F4.
e. Find the ratio of your predicted frequency of the note F4 to your predicted frequency of the note E4. Compare the ratio to the base of your model. Why does your comparison make sense?

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A-3 FR4 G4 Table 38 Frequencies of Some Notes on a Piano Number of Notes above A3 Frequency (in hertz) Note АЗ A#3 B3 C4 233.1 246.9 261.6 277.2 293.7 311.1 329.6 D4 D#4 E4 F4 F#4 370.0 392.0 415.3 440.0 10 G#4 A4 12