Question

part 2: move arms up and down twice every second. move arms the same vertical distance as in part 1. compare the periodic waves she makes in each part of the workout. from part 1 to part 2 of the workout, the frequency, the wavelength, and the amplitude. the energy transferred down the rope every second. related content do 4 problems skip check

Explanation:

Step1: Define frequency

Frequency is the number of wave - cycles per second. In part 1, assume the number of arm - movements (and thus wave - cycles) per second is $n_1$. In part 2, the number of arm - movements per second is $n_2 = 2n_1$. So the frequency increases.

Step2: Recall wave - speed formula

The wave - speed formula is $v=\lambda f$, where $v$ is the wave speed (constant in this case as the medium and conditions are the same), $\lambda$ is the wavelength and $f$ is the frequency. Since $v$ is constant and $f$ increases, from $\lambda=\frac{v}{f}$, the wavelength decreases.

Step3: Analyze amplitude

The amplitude is the maximum displacement from the equilibrium position. Since the vertical distance of arm - movement is the same in both parts, the amplitude remains the same.

Step4: Consider energy in a wave

The energy transferred by a wave per second is proportional to the square of the amplitude and the square of the frequency ($E\propto A^{2}f^{2}$). Since the amplitude is the same and the frequency increases, the energy transferred down the rope every second increases.

Answer:

Increases, Decreases, Remains the same, Increases