Question

a woman is exercising with heavy ropes. she moves her arms up and down in a repeating pattern, sending waves down the ropes as shown below. the instructions for the first two parts of her workout are: - part 1: move arms up and down once every second. move arms vertically from shoulder to waist level. - part 2: move arms up and down once every second. move arms vertically from head to knee level. 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. (options: increases, decreases, stays the same)

Explanation:

1. Frequency: Frequency is the number of oscillations per unit time. In both Part 1 and Part 2, she moves her arms up and down once every second. So the frequency (number of waves per second) remains the same.
2. Wavelength: Wavelength is the distance between two consecutive identical points on a wave. Since the frequency is the same and the medium (the rope) is the same, the speed of the wave ($v = f\lambda$, where $v$ is speed, $f$ is frequency, $\lambda$ is wavelength) remains constant. As frequency ($f$) is constant, wavelength ($\lambda$) also stays the same.
3. Amplitude: Amplitude is the maximum displacement from the equilibrium position. In Part 1, the arm movement is from shoulder to waist, and in Part 2, it's from head to knee. The vertical distance moved in Part 2 is greater, so the amplitude (maximum displacement of the wave) increases.
4. Energy Transferred per Second: The energy of a wave is related to its amplitude (and frequency, but frequency is constant here). Since amplitude increases, the energy per wave increases. And since frequency (waves per second) is constant, the total energy transferred per second (power) increases.

Answer:

• Frequency: stays the same
• Wavelength: stays the same
• Amplitude: increases
• Energy transferred down the rope every second: increases