Question

Someone please help me with this.

The speed of ocean waves depends on their wavelength λ (in meters) and the gravitational field strength g (in m/sˆ2) in this way:

V=Kλˆp Gˆq

Where K is a dimentionless constant. Find the value of the exponents p and q.


This is a dimensional analysis problem. If g and λ are the only quantities that can affect the speed (ocean depth is actually another, but we will assume a very deep ocean), then some combination
V * λ^-p * g^-q must be a dimensionless constant, K. The length dimension exponent of the product is 1 -p -q = 0 and the time dimension exponent is -1 +2q = 0.
This leads to -1/2 + q = 0
1/2 - p = 0
p = 1/2 q = 1-p = 1/2
V = K λ^1/2 g^1/2

Answer 1

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