Question

question 8 (multiple choice worth 3 points) ou.01the diagram below shows the distance traveled by two light waves in 1 second. based on the diagram, which of these conclusions is correct? the frequency of wave 1 is double the frequency of wave 2. the frequency of wave 2 is double the frequency of wave 1. the wavelength of wave 1 is four times the wavelength of wave 2. the wavelength of wave 2 is four times the wavelength of wave 1.

Explanation:

1. Recall the relationship between wavelength ($\lambda$), frequency ($f$), and speed ($v$): $v = \lambda f$. For light waves, the speed $v$ is constant (speed of light, $c$).
2. From the diagram, both waves travel the same distance in 1 second, so they have the same speed ($v_1 = v_2 = c$).
3. Count the number of cycles (wavelengths) in the diagram: Wave 1 has, say, $n_1$ cycles, Wave 2 has $n_2$ cycles. Visually, Wave 2 has more cycles (higher frequency) than Wave 1. Let's assume Wave 1 has 4 cycles and Wave 2 has 8 cycles (or similar ratio).
4. Frequency is the number of cycles per second. So if Wave 2 has double the number of cycles (wavelengths) in the same distance (same speed), then $f_2 = 2f_1$ (since $v = \lambda f$, and $v$ is constant, more cycles mean higher frequency, shorter wavelength).
5. Analyze the options:

• "The frequency of Wave 1 is double the frequency of Wave 2": Incorrect, Wave 2 has higher frequency.
• "The frequency of Wave 2 is double the frequency of Wave 1": Correct, as Wave 2 has more cycles (higher frequency) and if the speed is the same, frequency and wavelength are inversely proportional.
• "The wavelength of Wave 1 is four times the wavelength of Wave 2": If Wave 2 has double the frequency, wavelength of Wave 1 would be double (not four times) that of Wave 2 (since $\lambda \propto \frac{1}{f}$).
• "The wavelength of Wave 2 is four times the wavelength of Wave 1": Incorrect, higher frequency means shorter wavelength, so Wave 2's wavelength is shorter.

Answer:

The frequency of Wave 2 is double the frequency of Wave 1. (Assuming the option is labeled as, e.g., "The frequency of Wave 2 is double the frequency of Wave 1" among the choices)