Wave Speed in Water: Find Wave Speed Given Tub Width & Frequency

[asz304]

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

 

[tiny-tim]

hi asz304!

(have a lambda: λ )

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 got to be two nodes in each wavelength!

(alternatively: one side is a peak when the other side is a trough, but a wavelength is peak to peak)

 

[asz304]

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

 

[tiny-tim]

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

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

 

[asz304]

Thanks :D.