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Directions: Read the passage about waves of different wavelengths, frequencies, and amplitudes.

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.

1 answer

To determine which statement correctly compares the energies of the waves shown in Graph 2, we would analyze the properties of the waves based on the information provided in the passage.

From the passage, we know that the energy of a wave is related to its amplitude and frequency. Specifically:

  1. The energy of a wave is proportional to the square of its amplitude.
  2. The amount of energy transferred by the wave is proportional to its frequency.

Since we don't have visual graphs in this format, let's assume the following hypothetical situations based on typical wave analysis:

  • If we visualize the graphs and find that Wave X has a smaller amplitude than Wave Y but greater frequency, we might conclude that Wave Y has more energy due to higher amplitude even if Wave X has a high frequency.
  • If Wave Z has a higher amplitude than both Wave Y and Wave X but a similar frequency to Wave Y, then Wave Z would have the highest energy.

Assuming typical comparisons found between waves based on amplitude and frequency for a logical conclusion:

Without the specifics regarding the amplitudes and frequencies of each wave from Graph 2, it's challenging to determine the exact correct answer. However, the answer can usually be deduced if we compare relative amplitudes and frequencies as follows:

If you find that:

  • Wave Y has a low amplitude, and Wave X has higher amplitude than Y, you would choose "B. Wave Y has less energy than wave X."
  • Conversely, if Wave Y was determined to have greater amplitude than both, then statement "C. Wave Z has less energy than Y" may fit if Z indeed has lower amplitude than Y.

If I have to pick one answer based just on provided options without assumptions,

  • If the context allows, "A. Wave X has less energy than wave Z" could also be appropriate first choice depending on their comparative values.

Ultimately, because we are not appraising the visual graphs directly, I suggest the answer depends on those visuals. However, based on analysis of wave properties, the correct answer considering general knowledge of waves would likely align with amplitudes or frequency impact assessment against the provided statements.