Physics Homework....

DeathByMonkeys

United States742 Posts

January 03 2009 20:16 GMT

A standing wave resonates at 400 Hz with three antinodes on a string tied tightly between two posts 2.0 meters apart.

What is the wavelength of this standing wave?

It seems like I've either over simplified it or over complicated it in my mind. Since the posts are 2m apart couldn't I assume that the wavelength is 1m? Or I could roll with...

λ = v/f

But then I have one variable in a three variable equation (λ = v/400Hz).

The last part of the question asks "What is the fundamental frequency of the string?" but I haven't thought about that one yet.

robice

Germany114 Posts

January 03 2009 20:27 GMT

λ = v/f is the De-Broglie wavelangth.
It is only for describing the wavelength of matter (such as electrons etc.)

In this case (electromagnitc radiation), you get the wavelength = 2full antinodes.

2m ~ 3antinodes
=> 4/3m ~ 2antinodes = wavelength
You dont even need the frequency of 400 Hz.

Edit: Its no radiation, i did overread string first... But the result is the same

micronesia

United States24495 Posts

January 03 2009 20:31 GMT

Draw a picture. It will help you a lot (robice probably did the same thing when he/she was first learning it). If you can't draw the picture you need to learn more about fundamental properties of waves, and then try this again.

robice

Germany114 Posts

January 03 2009 20:40 GMT

Dont let you fool and draw no picture

Im pretty sure you can imagine this.
It happens often that you oversee the easiest solution, then take difficult formulas and are stuck.

micronesia

United States24495 Posts

January 03 2009 20:42 GMT

On January 04 2009 05:40 robice wrote:
Im pretty sure you can imagine this.

He may be able to imagine it, or he may not. If so, then yeah he shouldn't bother drawing the picture... but if he does it's no big deal.

If not, then he won't be able to solve this. However, if he goes ahead and draws the picture, it will reinforce how this all works until he gets to a level where he can do this without drawing a picture.

In other words, there is not much of an advantage to pointedly avoiding drawing the picture.

robice

Germany114 Posts

January 03 2009 20:50 GMT

The point is that he knows already about the De-Broglie formula for wavelength, so he probably is far ahead of drawing pictures like this and probably just mixed things up.

If you really cant imagine this string with 3 antinodes between 2 posts, draw the picture.

boezou

United States56 Posts

January 03 2009 21:35 GMT

anyways robice has the right answer, the wavelength (since it has 3 antinodes) would be
2/3 of 2, which is 4/3

using this wavelength, the given freq, and λ = v/f you can find v- which a property unique to the string
(v is the phase speed of the wave and in a string is also the sqrt of the Tension/the linear density--that's not really important though)
anyways, use this v (which =1600/3) and find the freq that would given you the fundamental wavelength--which is basically the longest wavelength that the string can vibrate at--which is the case where there's only one antinode. basically a stand wave with the whole string moving together up on down. This correspends to a wave length of
4m (x2 the length of the string)

so the fundamental freq= 400/3 (v/4)
sorry this was so long, i'm too wordy sometimes

Luddite

United States2315 Posts

January 03 2009 21:55 GMT

On January 04 2009 05:50 robice wrote:
The point is that he knows already about the De-Broglie formula for wavelength, so he probably is far ahead of drawing pictures like this and probably just mixed things up.

If you really cant imagine this string with 3 antinodes between 2 posts, draw the picture.

But... that's not the formula for De-Broglie wavelength, and since when are you "ahead of drawing pictures"?

HeavOnEarth

United States7087 Posts

January 03 2009 22:31 GMT

we're doing this in chem o_O

robice

Germany114 Posts

January 04 2009 13:56 GMT

#10

+ Show Spoiler +

On January 04 2009 06:55 Luddite wrote:

Show nested quote +

But... that's not the formula for De-Broglie wavelength, and since when are you "ahead of drawing pictures"?

λ = v/f is the De-Broglie formula for the wavelength of matter as it is equivalent to p = h/λ.
Its just a formula to bring the speed of moving matter (especially electrons) in context to a wavelength.
Doesnt belong to the question of the OP anyways, but if you want me to explain the transition from λ = v/f to p = h/λ (3 simple steps) then pm me.

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