Sound waves from a basketball. Refer to the American Journal of Physics (June 2010) study of sound waves in a spherical cavity, Exercise 2.43 (p. 80). The frequencies of sound waves (estimated using a mathematical formula)

resulting from the first 24 resonances (echoes) after striking a basketball with a metal rod are reproduced in the following table. Recall that the researcher expects the sound wave frequency to increase as the number of resonances increases.

a. Hypothesize a model for frequency (y) as a function of number of resonances (x) that proposes a linearly increasing relationship.

b. According to the researcher’s theory, will the slope of the line be positive or negative?

c. Estimate the beta parameters of the model and (if possible)
give a practical interpretation of each.

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Resonance Frequency 123456789 979 2 1572 2113 2122 2659 2795 3181 3431 3638 10 3694 11 4038 12 4203 13 4334 14 4631 15 4711 16 4993 17 5130 18 5210 21 23 222222 19 5214 20 5633 5779 5836 6259 24 6339