Question

another way maya gets a more intense workout is by moving her arms faster to make the waves crests closer together. in this graph, the blue line models a wave maya created with a battle rope earlier in her workout. the orange line models another wave she creates by moving her arms faster. complete the sentences. when maya moves her arms up and down faster, she decreases the and increases the of the wave. as a result, mayas workout is more intense, which means the energy of the waves she creates

Explanation:

Step1: Analyze the wave - length

The wavelength of a wave is the distance between two consecutive crests (or troughs). When Maya moves her arms faster, the crests (or troughs) of the wave are closer together. From the graph, we can see that the orange line (faster - moving - arms wave) has a shorter wavelength compared to the blue line.

Step2: Analyze the frequency

The frequency of a wave is the number of complete waves that pass a given point in a unit of time. A shorter wavelength implies a higher frequency. Mathematically, the relationship between the speed \(v\), wavelength \(\lambda\), and frequency \(f\) of a wave is \(v = f\lambda\) (assuming the speed of the wave in the medium is constant).

Step3: Analyze the energy

The energy of a wave is related to its frequency. The formula for the energy of a wave (for a simple harmonic wave) is \(E\propto f^{2}\) (for non - quantum mechanical waves, in a more general sense, higher - frequency waves carry more energy).

Answer:

When Maya moves her arms up and down faster, she decreases the wavelength and increases the frequency of the wave. As a result, Maya's workout is more intense, which means the energy of the waves she creates increases.