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Wave speed in water.

  • Thread starter asz304
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  • #1
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Homework Statement


When you slosh the water back and forth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 64.6 cm wide tub is 0.835 Hz. What is the speed of the water wave?


2. The attempt at a solution

v= lambda*f

L = 1/2 lambda

v = 2L*f

v= 1.07 m/s

My Question:

Why is the width of the bathtub 1/2 the wavelength?
I'm confused.

Thanks
 

Answers and Replies

  • #2
tiny-tim
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hi asz304! :smile:

(have a lambda: λ :wink:)
When you slosh the water back and forth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center.

Why is the width of the bathtub 1/2 the wavelength?
there's gotta be two nodes in each wavelength! :smile:

(alternatively: one side is a peak when the other side is a trough, but a wavelength is peak to peak)
 
  • #3
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It's getting a bit clearer.
So a node is like a point in the maximum?
Silly question: Where does it say in the question that the wave has only 1 wavelength?

Thanks
 
  • #4
tiny-tim
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So a node is like a point in the maximum?
no, a node is stationary …

sloshing to the right, sloshing to the left, but no sloshing at the node :smile:
Where does it say in the question that the wave has only 1wavelength?
it doesn't

the definition of a wavelength is the length from peak to peak …

if you can only see one peak and one trough, you have to double that to get peak to peak :wink:
 
  • #5
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Thanks :D.
 

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