Waves in a water tank

Let's take a look!

What type of experiment is this?

Experimental procedure and explanation:

• Standing waves in a water tank is called sloshing. A standing wave is a wave whose antinodes (where the amplitude is large) and nodes (where the amplitude is zero) do not move. Let’s conduct an experiment with these waves.
• We prepared a water tank 58 cm wide and 39 cm deep and filled it with water to a depth of approximately 15 cm, with coloring agents added to aid visualization.
• Move the rod up and down along the edge of the water surface to create waves. Ensure that the rod is vibrated sufficiently. When studying waves, it is essential to consider the wavelength (the distance between two peaks of a wave) and frequency (the number of vibrations per second). The period (the time it takes for one wave or time interval) is the reciprocal of the frequency (1 ÷ frequency).
• Vibrating the bar at regular intervals creates a standing wave. Changing the period by either speeding it up or slowing it down can alter the shape of the wave (called a mode). Typically, slower speeds produce longer wavelengths, while faster speeds generate shorter wavelengths.
• A consistent relationship exists between the waveform (mode) and the period (time interval) of a wave. The waveform (mode) that occurs during each period is fixed and can be calculated theoretically. Achieving a beautiful wave requires precise vibration of the rod for each period. If the wave appears messy or unclear, adjust the period to observe any changes in its shape.
• The waveform (mode) and period (time interval) can be expressed by the following equation. However, it is important to ensure that the water is deep enough as the calculation may not match if the water depth is too shallow.

• 
  Frequency   , Hz (hertz) is 1/s (number of times per second)）
  Period
  where a is the width (m), b is the depth (m), m is the order in the width direction (number of peaks to valleys or valleys to peaks), n is the order in the depth direction, g is the gravitational acceleration = 9.8 (m/s2), and π = 3.14.
• A sample calculation of this equation is shown in the figure, which illustrates the waveform and period for a water tank with a width of a = 0.58 m (58 cm) and depth of b = 0.39 m (39 cm). Regular vertical movement at this period (time interval) generates a wave of that waveform (mode). Therefore, the shape of the wave is determined by the period of the vertical movement, not by the manner of pushing. Try moving an area at the end of the water tank up and down; alternatively, you can try this in a bathtub and calculate it based on its size.
  
• This video of the experiment was produced with the support of JSPS KAKENHI 18K03956.

[Keywords]

Waves, sloshing

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