Refer to the American Journal of Physics (June 2010) study of sound waves in a spherical cavity, Exercise 2.43 (p. 52). 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.
Resonance ______________________________Frequency
1..................................................................979
2................................................................1572
3................................................................2113
4................................................................2122
5................................................................2659
6................................................................2795
7................................................................3181
8................................................................3431
9................................................................3638
10................................................................3694
11................................................................4038
12................................................................4203
13................................................................4334
14................................................................4631
15................................................................4711
16................................................................4993
17................................................................5130
18................................................................5210
19................................................................5214
20................................................................5633
21................................................................5779
22................................................................5836
23................................................................6259
24................................................................6339
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.