12 December 2005

The Doppler Effect for Dummies

AKA Ball Bashing.

Well, for Doris actually - hardly a dummy, but here we go.

Hello Doris.

Imagine I am 100 miles away from you and we are both standing completely still.

Because its Christmas, I am utilising my magic, umbrella style, multidirectional tree bauble gun, and its shooting out lovely Christmas tree baubles in every direction. No problem, they're quite light and shatterproof.

This grand emission happens once every minute. Because I am superwoman and I said so.

They are all travelling at exactly 100 miles an hour, so, barring obstructions, the first of my luvverly glittery tree balls zooming out in your direction, is going to land in your lap exactly one hour after I shot it at you.

Right?

Thats because it will need the hour to travel the 100 miles between us.

Because we both remain still, the next ball will take just as long, leaves me a minute after the first one and so gets to you exactly a minute after the first one lands. And so on.

Fine so far. In a formula, the frequency with which you get hit by my yuletide baubles, f', is exactly the same as the frequency that my magical umbrella thingy lobs them out, f0.

f' = f0.

So, now I start steaming towards you at ten miles a minute. I am still chucking out balls at one a minute from my perspective, but the second one only has ninety miles to travel. The third one only has eighty miles to travel. So they hit you slightly quicker each time, right?

If I was running away from you (or more likely, you were running from me) so we instead got further apart from each other by ten miles a minute, then the second ball would have to cover 110 miles, the third 120 miles, etc etc and although I let 'em rip exactly a minute apart, they would take more than a minute between balls to reach you, because each one has to travel progressively further.

Boring maths bit

If:
V = velocity of a christmas tree ball (100 miles an hour) and
Vs = equals the velocity of the source of the balls (ie me), and
V0 = equals the velocity of the observer (ie you, and in this case thats a zero, unless you have begun running away already,) then



See, V/V = 1, always. So if we both stay still, f' = f0(1)

End of boring maths bit


This works for anything with a frequency, like wave forms. That means light, sound.

It doesn't matter what the frequency is at the source (me and my umbrella thingy), if you and I are getting closer, no matter which one of us is moving (could be both), then whatever is being emitted, will accost your senses at a higher frequency than that. White light appears bluer, fire engine nee-naws sound higher pitched. Higher perceived frequency.

If we are moving apart then the perceived frequency drops; white light looks reddish, fire engine noise becomes a lower drone.

Of course, If I was travelling faster than 100 miles an hour, ie faster than my magic baubles, I would break through the ball barrier, and be behind you before you even got hit.

But that's another story.

The posh scientific version here.

10 comments:

zilla said...

"I would break through the ball barrier, and be behind you before you even got hit."

You are my favorite kind of feminist!

Carol said...

Gosh

doris said...

I am conjugating and digesting and finding that I am enjoying this easy to digest appetiser. It is leading me nicely towards the next course :-)

Your explanation (of pelting me with Christmas baubles) was easy to follow and then led me into seeing how this can be applied to light, light waves and red shift and blue shift. I already know that the establishment use the redshift as a way of showing that the universe is expanding and therefore supports the Big Bang theory.

I am stuck a little on fully 'getting' the maths and will need to re-read and think about it even more. I thought the link you gave was very helpful and I liked the graphics.

I still have a problem with the redshift in connection with the Big Bang theory but until I can verbalise my questions I am stuck in a loop of not quite grasping. I reckon part of my problem is because I want to understand it all and want to see the whole jigsaw before I have managed to piece together and understand some of the smaller segments.

It is also possible that the way these things are taught is not in an accessible way. For example, when I learned about certain equations in school, it would have helped if I understood a practical application for these things. I can do the equations because I know the rules (or at least used to know them!) but understanding what it really meant just eluded me.

The ball is in my court to find out and I can do that now because I choose to.

Thank you so very much for going to all this effort. You used Doppler so efortlessly in your earlier post that I had a feeling you could explain it. I take my hat off to you :-)

PS. Can I give you a list of other concepts I would like explained? ;-) (only joking!!!)

fineartist said...

Anybody got any pain meds? My head hurts now. Heee.

I believe you lost me when the first ball flew. Am scheduled to re read post in one minute, please don't fire any more balls till I get there.

Milt Bogs said...

I would be very grateful if you could shoot a few of those baubles my way.

Homebase have run out.

bulb said...

eh yeah. I lost you at: magic, umbrella style, multidirectional tree bauble gun"

Want one of those.

ME Strauss said...

So I can say that Cheryl is a real ball buster and she uses umbrellas to do it. right? I like your version way better than the posh scientific version. Cheryl is easier to spell than Doppler.

Cheryl said...

Zilla
I asked my husband if he thought I was a feminist. He said no, no moustache. So I continue to be covert......

Doris - ouch! Intellectualism on my blog? What, you want me to think, or something? No fair.

Milt - try good old Woolies. Je prefer le Pound Shop.

Steve said...

Sounds like a load of balls to me

Ally said...

This has cleared things up no end for me. I always KNEW it was what made the stars go 'worra worra worra' as The Enterprise flew past them; but I could never understand quite why.

Can we do Faraday's Cage next week?