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Homework Help: Find values of p & q in v=K(lambda^p)(g^q)

  1. Aug 27, 2011 #1
    1. The problem statement, all variables and given/known data
    The speed of ocean waves depends on their wavelength lambda (measured in meters) and the gravitational field strength g (measured in m/s^2) in this way:
    where K is a dimensionless constant. Find the values of the exponents p and q.

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Aug 27, 2011 #2


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    Homework Helper

    this is a units or dimension question.

    Suppose p was 3 and q was 5

    then V = K.L^3.g^5 [it was shorter to type L than spell out lambda]

    Look at the units.
    L^3 would have units m^3
    g^5 would have units m^5.s^-10

    combines that makes m^8.s^-10

    But this is velocity!!!! so the units would be m.s^-1 so 3&5 are certainly not the values.

    What should they be?
  4. Aug 28, 2011 #3
    Am I looking for actual numbers?
    The way I understand it, is that how quickly (how many meters per second) the crest of a wave moves across a distance depends on how far apart the crests are (in meters), then multiplied by the gravitational pull. The gravitational pull is measured in meters/second^2. I don't really understand the idea of gravitational pull being measured in meters per second^2. Also I don't understand why wavelength and gravitational pull are exponentiated.
    You say that this is a dimensions or units question, which means I need to convert from one unit to another I guess, but I don't see what it is I am converting. We just have meters, and meters over seconds, and the answer is supposed to be meters over seconds, so what is the problem?

    Thank you for your help thus far,
  5. Aug 28, 2011 #4


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    Homework Helper

    Acceleration units can be confusing, because of the way we just bunch similar units together - that is why the m/s^2. For understanding it is not metres per second squared, even though it is written like that.

    If you used a stop watch in a car, you might measure that it reached 60 km/h in 5 seconds.
    That represents an average acceleration of 12 (km/h)/s or 12 kilometres per hour per second

    I will use a comma to show where we pause when reading that:

    Kilometres per hour, per second.
    Seems clear but if we pause in the wrong place we would say

    kilometres, per hour per second which sound like gobbledy-gook.

    The real problem arises if the cars speedometer was calibrates in metres per second instead of kilometres per hour.
    You might measure that the car accelerated to 15 m/s in 5 seconds.

    That would mean an acceleration averaging 3 m/s each second - or 3 metres per second per second.
    When written in english, with the comma [pause] for emphasis that is

    3 metres per second, per second

    However in symbols we write that m/s^2 the exponent indicating per second occurred twice.

    If you multiply wavelength [m] by g [m/s^2] we get dimension/units of m^2/s^2, which can be written as (m/s)^2
    That means lambda x g gives the square of speed.
    to get just speed, we need the square root of that - and square root is shown as ^0.5

    eg 9^0.5 = 3 [or -3]

    so if the exponents in the original formula were both 0.5, the dimensions would be fine.
    Last edited: Aug 28, 2011
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