MS-PS4-1: Use mathematical representations to describe a simple model for waves that includes how the amplitude of a wave is related to the energy in a wave.

Clarification Statement: Emphasis is on describing waves with both qualitative and quantitative thinking.

By the end of grade 8. A simple wave has a repeating pattern with a specific wavelength, frequency, and amplitude. A sound wave needs a medium through which it is transmitted. Geologists use seismic waves and their reflection at interfaces between layers to probe structures deep in the planet.

Evidence Statements

MS-PS4-1

1. Representation

   1. Students identify the characteristics of a simple mathematical wave model of a phenomenon, including:

      1. Waves represent repeating quantities.

      2. Frequency, as the number of times the pattern repeats in a given amount of time (e.g., beats per second).

      3. Amplitude, as the maximum extent of the repeating quantity from equilibrium (e.g., height or depth of a water wave from average sea level).

      4. Wavelength, as a certain distance in which the quantity repeats its value (e.g., the distance between the tops of a series of water waves).

2. Mathematical modeling

   1. Students apply the simple mathematical wave model to a physical system or phenomenon to identify how the wave model characteristics correspond with physical observations (e.g., frequency corresponds to sound pitch, amplitude corresponds to sound volume).

3. Analysis

   1. Given data about a repeating physical phenomenon that can be represented as a wave, and amounts of energy present or transmitted, students use their simple mathematical wave models to identify patterns, including:

      1. That the energy of the wave is proportional to the square of the amplitude (e.g., if the height of a water wave is doubled, each wave will have four times the energy).

      2. That the amount of energy transferred by waves in a given time is proportional to frequency (e.g., if twice as many water waves hit the shore each minute, then twice as much energy will be transferred to the shore).

   2. Students predict the change in the energy of the wave if any one of the parameters of the wave is changed.