Instructions: Read the passage discussing waves with varying wavelengths, frequencies, and amplitudes.

Question

A student is curious about the reasons behind the differences in volume and pitch among sounds. To explore this, he embarks on research to uncover the wave properties responsible for these variations.

Initially, he grasps that a wave constitutes a recurring pattern characterized by specific wavelength, frequency, and amplitude. The amplitude of a wave represents the maximum distance above or below the equilibrium point. The energy of a wave is determined by squaring its amplitude. Frequency denotes how often the wave pattern repeats, and the energy transferred by the wave is proportional to its frequency. For instance, in sound waves, the amplitude correlates with loudness, while frequency correlates with pitch.

During his investigation, the student encounters graphs that aid his comprehension of how wave properties influence their energy.

Graph 1 depicts the amplitudes (measured in meters) of three waves (labeled wave 1, 2, and 3) as they travel through a medium over time (measured in seconds).

Graph 2 displays an alternative set of three waves (labeled as wave X, Y, and Z) traversing through a medium.



Which statement accurately contrasts the energies of the waves depicted in Graph 2?

(1 point)
Responses

Wave Y has less energy than wave X.
Wave Y has less energy than wave X.

Wave X has less energy than wave Z.
Wave X has less energy than wave Z.

Wave Z has less energy than wave X.
Wave Z has less energy than wave X.

Wave Z has less energy than wave Y.

Answer 1

To accurately contrast the energies of the waves depicted in Graph 2, we need to consider the properties of amplitude and frequency, as these directly affect the energy of waves.

Since the passage states:

• The energy of a wave is determined by the square of its amplitude.
• The energy transferred by the wave is also proportional to its frequency.

Without the specific details of Graph 2, we cannot definitively evaluate the energies of waves X, Y, and Z based on their visual attributes.

However, if we assume that:

• Graph 2 indicates varying amplitudes for the waves, the wave with the largest amplitude would have the most energy.
• If frequencies are visibly different, the wave with the highest frequency would also possess higher energy.

From the options provided:

1. Wave Y has less energy than wave X.
2. Wave X has less energy than wave Z.
3. Wave Z has less energy than wave X.
4. Wave Z has less energy than wave Y.

To determine the correct statement, we would ideally identify the amplitudes and frequencies of each wave in Graph 2. If we assume wave X has larger amplitude or frequency than wave Y, then statement 1 might be applicable. If wave Z has the largest amplitude/frequency compared to wave X, statement 2 could apply.

Given no specific data about the amplitude or frequency from Graph 2, we are unable to make an accurate comparison.

However, based on the logical structure of waves:

• If wave Z has a smaller amplitude than wave X, then Wave Z has less energy than wave X would be correct.

Answer: Wave Z has less energy than wave X.