You go visit your friend, Sallie Geek, at Calpoly San Luis Obispo. She asks you

Question

You go visit your friend, Sallie Geek, at Calpoly San Luis Obispo. She asks you to go
scuba diving with her in Pismo Beach. She knows you took physics 132 at Calpoly
Pomona. While sitting at the beach preparing for the dive, she tells you that a gas
bubble from a deep explosion under water oscillates with a period T = K(p^a)(p^b)(E^c)
where K is a constant with no unit, p is the static pressure, p the water density,
and E the total energy of the explosion. Find a, b, and c.

Please show work. I will check back in a few hours to rate the best answer.

Explanation / Answer

so we can do unit checking

left side has units seconds

right side is (N/m^2)^a*(kg/m^3)^b*(J)^c = ( kg/(m s^2)^a*(kg/m^3)^b( kg m^2/s^2)^c

so kg^(a+b+c) m^(-a-3b+2c) s^(-2a + 2c)

so a + b + c = 0 , -a -3b + 2c = 0 and -2a + 2c = 1

add first and second

-2b + 3c = 0 so b = 3/2 c

third equation a = c - 1/2

so c - 1/2 + 3/2 c + c = 0

7/2 c = 1/2

so c = 7, a = 6.5, b=10.5

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