Confused about definition of wavelength

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SUMMARY

The wavelength of a sinusoidal wave is defined as the spatial period, measured between two repeating points on the wave. In discussions regarding waves defined as functions of time, such as those of a simple harmonic oscillator, confusion arises between the concepts of wavelength and period. The period refers to the time taken for one complete cycle of the wave, while wavelength pertains to the spatial distance between repeating points. Understanding the relationship between time and frequency is crucial, as they are inversely related.

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  • Understanding of sinusoidal wave properties
  • Knowledge of simple harmonic motion
  • Familiarity with the concepts of wavelength and period
  • Basic grasp of wave frequency and its relationship to time
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V0ODO0CH1LD
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Wavelength of a sinusoidal wave is defined as the spatial period of the wave, which can be measured between any two points on the wave where the shape repeats. But if my wave is defined as a function of time (like those of a simple harmonic oscillator), how can you say the distance along the time axis is the wavelength? Am I measuring something else that just happens to be equal to the distance between two points in the same phase along the time axis? How can the time axis determine the wavelength of a wave? Also; isn't that distance the period? The amount of time it takes for the wave to complete one cycle? In which case the velocity of the wave would always equal one?
 
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V0ODO0CH1LD said:
Wavelength of a sinusoidal wave is defined as the spatial period of the wave, which can be measured between any two points on the wave where the shape repeats. But if my wave is defined as a function of time (like those of a simple harmonic oscillator), how can you say the distance along the time axis is the wavelength?

Who says it is a wavelength?

In that case, this is now known as the period of oscillation, which you stated later.

Zz.
 
But if my wave is defined as a function of time,,,,

you mean just like a sine wave?

Time relates directly to frequency...they are inverses...

If you don't get what I mean, just plot some waves and LABEL the axes you choose to use...
 

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