Waves: velocity, frequency, wavelength

[bleucat]

Homework Statement

If you slosh the water back and forth in a bathtub at the correct frequency, the water rises first at one end and then at the other. Suppose you can make a standing wave in a 135 cm long tub with a frequency of 0.31 Hz. What is the velocity of the water wave?

Homework Equations

I know $$v = f \lambda$$ and that $$f = \frac{1}{T}$$, with $$v$$=velocity, $$f$$=frequency, $$\lambda$$=wavelength, and $$T$$=period.

The Attempt at a Solution

Okay, so this looked easy enough, right?
I converted 135 cm to 1.35 m and multiplied 1.35 x .31. This isn't the correct answer, however, and I am rather stymied. Am I missing something easy?

 

[Snazzy]

I believe that the frequency represents the fundamental frequency, ie. the bathtub length is half a wavelength.

 

[Moetasim]

I would first like to commend you for attempting to solve this problem on your own and for recognizing the relevant equations. However, it seems like you may have made a small error in your calculation. The equation for velocity of a wave is v = f * lambda, not v = f * lambda. So, the correct calculation would be 1.35 m * 0.31 Hz = 0.4185 m/s. This is the velocity of the water wave in the given scenario.

Additionally, it is important to note that the velocity of a wave is dependent on the medium through which it is traveling. In this case, the velocity of the water wave is specific to the bathtub and may not be the same in other mediums. Furthermore, the frequency and wavelength of the wave are also affected by the medium. So, if the bathtub was filled with a different liquid or if the wave was traveling through a different medium altogether, the velocity, frequency, and wavelength would all be different. This is an important consideration in any study of waves. I hope this helps in your understanding of the problem.