You are Here: Home >< Maths

# Dimensions of arguments of trigs and exponentials Watch

1. 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!
2. Say has dimension , then the PDE gives , but the RHS is just equal to , so whatever the dimensions of are, it's fine. That's assuming I haven't missed anything of course... but I don't think I have.
3. 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. .

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: December 17, 2010
Today on TSR

### Cambridge interview invitations

Has yours come through yet?

### Official Oxford interview invite list

Discussions on TSR

• Latest
• ## 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
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

## Groups associated with this forum:

View associated groups
Discussions on TSR

• Latest
• ## 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

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