Question

A transverse wave is shown here. Several wave properties are labeled with letters. Which of these statements accurately reflects the energy associated with the wave? Select ALL that apply.
Responses

A X is wavelength, and a decrease in X is associated with an increase in energy.X is wavelength, and a decrease in X is associated with an increase in energy.

B W is the amplitude, and a decrease in W is associated with an increase in energy.W is the amplitude, and a decrease in W is associated with an increase in energy.

C W is the amplitude, and an increase in W is associated with an increase in energy.W is the amplitude, and an increase in W is associated with an increase in energy.

D Y is the frequency, and an increase in Y is associated with an increase in energy.Y is the frequency, and an increase in Y is associated with an increase in energy.

E Z is the displacement, and a decrease in Z is associated with an increase in energy.

Answer 1

To evaluate the statements regarding energy associated with a transverse wave, let’s break down each option based on wave properties:

A. **X is wavelength, and a decrease in X is associated with an increase in energy.**
This statement is true; as the wavelength decreases, the frequency increases (since the speed of the wave is constant), and higher frequency waves carry more energy.

B. **W is the amplitude, and a decrease in W is associated with an increase in energy.**
This statement is false; an increase in amplitude (W) is associated with an increase in energy. Energy in mechanical waves is directly proportional to the square of the amplitude.

C. **W is the amplitude, and an increase in W is associated with an increase in energy.**
This statement is true; as mentioned, the energy is proportional to the square of the amplitude, meaning an increase in amplitude results in more energy.

D. **Y is the frequency, and an increase in Y is associated with an increase in energy.**
This statement is also true; higher frequency waves carry more energy, in line with the energy-frequency relationship.

E. **Z is the displacement, and a decrease in Z is associated with an increase in energy.**
This statement is false; displacement (which typically refers to the position of a point on the wave from equilibrium) doesn’t have a direct correlation with energy in the same way amplitude does.

Based on this evaluation, the accurate statements reflecting energy associated with the wave are:

- **A** (X is wavelength, and a decrease in X is associated with an increase in energy.)
- **C** (W is the amplitude, and an increase in W is associated with an increase in energy.)
- **D** (Y is the frequency, and an increase in Y is associated with an increase in energy.)