Some physics calculations.

Hello experts.
I need to impress a girl by helping her cousin out with some physics calculation
(never in my life I though I would write that sentence =),
though it was a looong time ago I tried to solve anything like this.
Maybe you guys can help me out, should be a piece of cake. ;)

Questions:
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1. A microwave oven discharges microwaves with a frequency of 2.45 GHz.
a) Determine the wavelength of the microwaves.
b) Determine the energy of the microwaves.
c) At a certain point of time, 3 x 10^26 photons / sec are produced.
    What is the effect of the microwave?

2. A violin cord is 32.5 cm long. The E-cord has a frequency of 660Hz, how much shorter do you have to cut it so it gives an A-tone (880Hz)?

I know these questions are elementary but my mind has hidden my knowledge very deep it seems...
Thanks for the help guys!  
Best regards
//Jide
LVL 1
jide85Asked:
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a_bCommented:
1.
a) wavelength  = 3 * 10^8 m/s / 2.45GHz
b)  Energy = Planck's constant x frequency(2.45GHz)
c)  Unsure what you mean by effect of the microwave


                   
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a_bCommented:
Not sure about 2, but I think you can apply the same formula - speed of sound = length * frequency
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byundtMechanical EngineerCommented:
When looking at a_b's first comment for question 1 a, it is important to make the units consistent--1 GigaHertz equals 1 billion Hertz.

When looking at a_b's first comment for question 1 b, you will need to look up the value for Planck's constant. There are two forms of it, differing by a factor of 2 pi. The one you need has a value of 6.62 × 10^-34 Joule seconds. Though the equation looks pretty simple, it was a revolutionary insight at the time. Planck examined results of careful experiments measuring the energy increase when shining infra-red light on small particles. He was amazed to find that the increase in energy was not continuously variable, but rather changed in stairstep fashion, albeit with very small steps. Classical physics couldn't explain these small steps, so Planck hypothesized the existence of what came to be called photons to explain it, with each photon possessing the energy shown by a_b's equation. This realization was a key step in the creation of quantum mechanics, and resulted in Planck winning the Nobel prize for Physics in 1918.

When trying to calculate the effect of the microwave in question 1 c, you are really calculating the amount of energy contained in all those photons. So multiply the Joules/photon you calculated in question 1 b by the photons/second. It is worth noting that 1 J/s equals 1 Watt.

For question 2, you should apply the formula in a_b's second comment. You don't need to know the speed of sound--just set the first frequency times the known length equal to the second frequency times the unknown length. Solve the resulting equation. The violinist has to solve this equation in realtime by moving his fingers up and down the strings to hit the right notes.
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jide85Author Commented:
Thanks a lot guys.
Specially to byundt who beautifully explained some history around it as well.
You guys rule!
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jide85Author Commented:
That is so true WaterStreet!
Sorry about the assignment question, I wont do it again. =(

I big thanks to byundt who really should think about using his talent for teaching.
Or maybe you already are?
Best regards
/Jide
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byundtMechanical EngineerCommented:
jide85,
There is nothing wrong with asking homework questions in Experts-Exchange. People do it all the time. Just be sure that you are up front about your purpose. That way, the experts trying to help will be in coaching mode rather than "here is the exact answer."

This thread (and how we ought to respond to it) was discussed extensively in a private forum by the Mods, Zone Advisors, Administrators and Page Editors. I don't normally look at Math & Science questions, but peeked into this thread due to the discussion. Rather than debate how we ought to handle it, I decided to lead by example.

Since you were trying "to impress a girl", I decided to augment the discussion with some background material. I'm glad you appreciated my efforts. Thanks for the kind words and grade!

Brad
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