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The image shows two students modeling a light wave by continuously moving the ends of the rope up and down.

(The energy travels to the right)

How would the waves change if the students continued moving the ends of the rope up and down the same distance but moved the ends faster?

answers:

The wavelength would increase and the amplitude would decrease, but the frequency would be unchanged.

The frequency would increase and the wavelength would decrease, but the amplitude would be unchanged.

The wavelength would increase and the frequency would decrease, but the amplitude would be unchanged

The amplitude would increase and the frequency would decrease, but the wavelength would be unchanged.

3 answers

When the students move the ends of the rope up and down faster while maintaining the same distance of movement, the frequency of the wave increases. This means that the waves are produced more frequently in a given time period.

According to the wave relationship, the speed of the wave (which remains constant if the medium does not change) is equal to the wavelength times the frequency (v = fλ). If the frequency increases and the speed remains constant, the wavelength must decrease.

With the amplitude remaining unchanged (since the distance moved up and down remains the same), the correct answer is:

The frequency would increase and the wavelength would decrease, but the amplitude would be unchanged.

are you sure

Yes, I am confident in that explanation. Here’s a more detailed breakdown to clarify:

  1. Frequency: This is how many wave crests (or cycles) pass a given point in one second. If the students move the ends of the rope faster, they are creating more wave cycles in the same amount of time, meaning frequency increases.

  2. Wavelength: This is the distance between consecutive crests (or troughs) of a wave. If the frequency increases and the speed of the wave remains constant, from the formula \( v = fλ \) (where \( v \) is wave speed, \( f \) is frequency, and \( λ \) is wavelength), we deduce that the wavelength must decrease.

  3. Amplitude: This is the height of the wave from its rest position (the maximum displacement). If the students continue moving the ends of the rope up and down the same distance, the amplitude does not change.

So the relationship is:

  • Increased frequency
  • Decreased wavelength
  • Unchanged amplitude

Thus, the correct answer is indeed:

The frequency would increase and the wavelength would decrease, but the amplitude would be unchanged.

Thank you for your patience, and if you have any more questions, feel free to ask!