Hey there! Sign in to join this conversationNew here? Join for free

Dimensions of arguments of trigs and exponentials Watch

    • Thread Starter
    Offline

    1
    ReputationRep:
    Hi,
    Quick question, do the arguments of trig functions and exponential functions have to always be dimensionless? I've been given four functions for y

    y = A sin (x - ut)
    y = A sin (x + ut)^0.5
    y = A sin (u - (x/t))
    y = A exp [-(x-vt)²]

    and I have to evaluate whether they're acceptable solutions based upon putting them back into the wave equation



    to see whether they work (which I've nearly done, the last one's a bit horrible), then the second step is evaluating this through 'another way', which I presume is looking at the argument. Problem is none of these have dimensionless arguments - they're [m], [m]^0.5, [m] and [m]² respectively, so does this mean none work? Because the maths with the first one implied it worked (unless my calculus was wrong, which is a serious possibility, but I doubt all four would be wrong!)

    Oops, that wasn't such a quick question after all. I hope someone could help me though! Thanks if so!
    • PS Helper
    Offline

    14
    Say y has dimension Q, then the PDE gives QL^{-2} = \dfrac{1}{(L/T)^2}QT^{-2}, but the RHS is just equal to QL^{-2}, so whatever the dimensions of y are, it's fine. That's assuming I haven't missed anything of course... but I don't think I have.
    Offline

    2
    ReputationRep:
    It seems clear enough that length has been non-dimensionalised in this question. Generally, there is supposed to be a wavelength L in these equations, e.g. \displaystyle y = A \sin \frac{2\pi (x - u t)}{L}.
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    What newspaper do you read/prefer?
    Useful resources

    Make your revision easier

    Maths

    Maths Forum posting guidelines

    Not sure where to post? Read the updated guidelines here

    Equations

    How to use LaTex

    Writing equations the easy way

    Student revising

    Study habits of A* students

    Top tips from students who have already aced their exams

    Study Planner

    Create your own Study Planner

    Never miss a deadline again

    Polling station sign

    Thinking about a maths degree?

    Chat with other maths applicants

    Can you help? Study help unanswered threads

    Groups associated with this forum:

    View associated groups
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

    Quick reply
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.