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.

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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 consider the properties of waves as described in the passage: amplitude and frequency. The energy transferred by a wave is proportional to both its amplitude (the height of the wave) and its frequency (how often the wave pattern repeats).

Since the passage doesn’t provide specifics about the graphs, I will outline the logic you should follow:

1. Identify Amplitude: Check the heights of waves X, Y, and Z. The wave with the highest amplitude will have the most energy.

2. Check Frequency: Also note how often the waves oscillate. A higher frequency can also contribute to greater energy output.

Now, to answer the question and compare the energies of waves based on their amplitudes and frequencies depicted in Graph 2, you will need to determine:

• Which wave has the largest amplitude?
• Which wave has the highest frequency?

Based on these considerations, you will analytically deduce which wave has the most energy.

Given the selections:

• 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.

Without the actual graphs, I can't definitively say which is correct. You need to refer to Graph 2 to determine the correct comparisons based on the amplitude and frequency of each wave. Just follow the logic discussed above!