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

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.

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 determine the correct statement about the energies of the waves shown in Graph 2, we need to consider both the amplitude and the frequency of the waves, as energy is related to these properties.

1. Amplitude: The energy of a wave is related to the square of its amplitude. Therefore, if one wave has a larger amplitude than another, it has more energy.

2. Frequency: The energy transferred by the wave is also proportional to its frequency; higher frequency waves have more energy than lower frequency waves.

Without seeing the specific characteristics of the graphs for waves X, Y, and Z, we can still analyze the statements provided based on the relationships mentioned above.

If we assume that:

• Wave X has the highest amplitude and/or frequency,
• Wave Y has a moderate amplitude and/or frequency,
• Wave Z has the lowest amplitude and/or frequency,

then the comparisons would look like this:

• A: If Wave X has more energy than Wave Z, this statement is incorrect.
• B: If Wave Y has less energy than Wave X, this might be correct depending on their amplitudes/frequencies.
• C: If Wave Z has less energy than Wave Y, this could also be correct if Wave Y has higher amplitude/frequency.
• D: If Wave Z has less energy than Wave X, this statement could also be correct if Wave X has the highest energy.

Given that without specific measurements or visuals, it's impossible to definitively say which one is correct based on the information provided.

You may need to refer back to Graph 2 to assess the amplitudes and frequencies of the waves depicted in order to identify correctly which wave has less or more energy than the others. If you can describe the properties of the waves, I might be able to help narrow it down!