Question

A student wonders why some sounds are louder than others and some music notes are softer and at a lower pitch than others. He decides to do some research to find out what properties of waves cause these changes.

First, he learns that a wave is a repeating pattern with a specific wavelength, frequency, and amplitude. The amplitude of a wave is the maximum distance above or below the equilibrium. The energy of one wave is found by calculating the square of the wave's amplitude. Frequency is the number of times the wave pattern repeats. The amount of energy transferred by the wave is proportional to its frequency. For example, in sound waves the amplitude of the wave is related to its loudness and the frequency is related to its pitch.

In his research, the student discovers some graphs that help him to understand how the properties of waves affect their energy.

Graph 1 shows the amplitudes (in meters) of three waves (labeled wave 1, 2, and 3) traveling through a medium over time (in seconds).



Graph 2 shows a different set of three waves (labeled wave X, Y, and Z) traveling in a medium.



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Multiple Choice Question
Which statement correctly compares the energies of the waves shown in Graph 2?
A.
Wave X has less energy than wave Z.

B.
Wave Y has less energy than wave X.

C.
Wave Z has less energy than wave Y.

D.
Wave Z has less energy than wave X.

Answer 1

To answer the question regarding the energies of the waves shown in Graph 2, we need to recall that the energy of a wave is proportional to the square of its amplitude and the frequency.

Since I do not have the specific visual representations of Graph 2, I can provide guidance on how to compare the waves.

1. **Identify the amplitudes of waves X, Y, and Z**: Look for the maximum height of each wave from the equilibrium point on the graph.

2. **Identify the frequencies of waves X, Y, and Z**: This can be discerned by measuring how many wave cycles occur in a given time period on the graph.

3. **Determine wave energies**: The energy will be calculated based on the amplitude squared and frequency. If we only have the amplitude information:
- Higher amplitude indicates more energy.
- Frequency also contributes to energy, so consider both if given.

With this understanding, you can determine which wave has more or less energy based on their amplitudes (and frequencies if visible) relative to each other.

Once you complete this analysis based on the visual data from Graph 2, you can then select the correct answer from the options provided. If you outline the amplitudes or frequencies, I'd be happy to assist you further in selecting the right option!