Increase Dipper Frequency - Wave Velocity & Pattern Changes

[Kyoma]

Homework Statement

A dipper moving up and down makes waves in a ripple tank.
What will happen when the dipper frequency is increased?

(a) The waves will be closer together.
(b) The waves will move more quickly across the tank.

2. The attempt at a solution

From the equation, velocity of wave = frequency of wave multiply by the wavelength, I choose (b) since when frequency is increased, so will the velocity. However, the answer is (a). Why? Why is velocity held constant?

 

[zhermes]

Good question Kyoma, this is a topic that is rarely explained well in intro physics classes. In situations like this (but not necessarily always) the velocity of propagation of a wave is a property of the material itself. I.e. the type/features of the wave don't matter, the velocity is always the same---because the water is the same. The wave-speed is a property of the water (for the record, this would be called a "non-dispersive" medium, because of this feature).

In your proposed solution you said that the, "frequency is increased"--you're right of course, and this is just another way of saying 'a'! Higher frequency means smaller wavelength (because of that equation---with constant velocity), and thus closer together wave-peaks.

Does that make sense?

 

[Kyoma]

So, there are some situations in which the velocity depends on the property of the material, then what kind of situations? Common sense?

 

[niklaus]

So, there are some situations in which the velocity depends on the property of the material, then what kind of situations? Common sense?

The velocity always depends on the material, for example the velocity of soundwaves in air is slower than the velocity of soundwaves in water, which is slower than the velocity in a solid. However, there are situations where the velocity also depends on the frequency. When this is the case we speak of a dispersive medium. An example of this is the breaking of light in a prism, where the velocity of the lightwaves moving through the prism depends on the frequency, thus leading to the refractive index depending on frequency, which, along with the geometry of the prism, leads to the spatial sparation of the components of white light.

 

[Kyoma]

I still don't understand, really.

I have checked a couple of physics forums. Some claimed that velocity of a wave will increase when frequency increases, while others claimed that velocity will always be held constant in a particular medium... :l

 

[niklaus]

In the cases that you will discuss in an introductory physics class, the velocity will remain constant independent of frequency. This is exactly true in some cases and only a (usually pretty good) approximation in others.
However, statement (a) of your original question is always true, whether you treat things exactly with more messy math or take the easy approximation.
If you want to see a more complete discussions of water waves, you can check out this Wikipedia page: http://en.wikipedia.org/wiki/Dispersion_(water_waves )