Waves: velocity, frequency, wavelength

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SUMMARY

The discussion centers on calculating the velocity of a standing wave in a 135 cm long bathtub with a frequency of 0.31 Hz. The correct formula to use is v = fλ, where v is velocity, f is frequency, and λ is wavelength. The user initially calculated the velocity by multiplying the length of the bathtub (1.35 m) by the frequency, but this approach is incorrect. The fundamental frequency indicates that the bathtub length represents half a wavelength, necessitating the use of the relationship λ = 2L for accurate calculations.

PREREQUISITES
  • Understanding of wave mechanics, specifically standing waves
  • Familiarity with the relationship between frequency, wavelength, and velocity
  • Knowledge of basic physics equations, particularly v = fλ
  • Ability to convert units (e.g., cm to m)
NEXT STEPS
  • Study the concept of standing waves and their formation in different mediums
  • Learn how to derive wavelength from the length of a medium in wave mechanics
  • Explore the implications of fundamental frequency in wave behavior
  • Practice problems involving wave velocity calculations using various frequencies and lengths
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Students studying physics, particularly those focusing on wave mechanics, as well as educators looking for examples of standing wave calculations in practical scenarios.

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

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