Compare Wave Energy - Middle School Physical Science

1. Identify which graph feature is most important for comparing energy when wave type is the same.

   Amplitude (height from equilibrium). Energy depends on amplitude squared, making it the key comparison factor.

2. Identify the amplitude on a graph if the trough is at $-8\ \text{mm}$ and equilibrium is $0\ \text{mm}$.

   $A = 8\ \text{mm}$. Amplitude is the absolute distance from equilibrium to trough.

3. Identify the error: "Amplitude equals the distance from crest to trough." What is the correction?

   Amplitude is half the crest-to-trough distance. Crest-to-trough is the full wave height; amplitude is only half that distance.

4. If Wave 1 has $A_1 = 2A_2$, what is the energy ratio $\frac{E_1}{E_2}$ (same wave type)?

   $\frac{E_1}{E_2} = 4$. Since $E \propto A^2$, doubling amplitude gives $2^2 = 4$ times the energy.

5. Two waves have amplitudes $5\ \text{mm}$ and $10\ \text{mm}$. Which carries more energy (same wave type)?

   The $10\ \text{mm}$ amplitude wave. Double amplitude means quadruple energy since $E \propto A^2$.

6. Which wave carries more energy if Wave 1 has amplitude $2\text{ cm}$ and Wave 2 has amplitude $1\text{ cm}$?

   Wave 1. Wave 1 has twice the amplitude, so it carries more energy.

7. What is amplitude on a wave graph (displacement vs. position or time)?

   Maximum displacement from the equilibrium (rest) line. Amplitude measures how far the wave moves from its rest position.

8. Identify the amplitude on a graph where trough is at $-8\text{ mm}$ and equilibrium is $0\text{ mm}$.

   $8\text{ mm}$. Amplitude equals the distance from equilibrium to trough (absolute value).

9. If Wave 1 has $A_1 = \frac{1}{2}A_2$, what is the energy ratio $\frac{E_1}{E_2}$?

   $\frac{E_1}{E_2} = \frac{1}{4}$. Halving amplitude gives $(\frac{1}{2})^2 = \frac{1}{4}$ the energy.

10. Find the energy ratio $\frac{E_1}{E_2}$ if amplitudes are $A_1=2A_2$ and $E\propto A^2$.

    $\frac{E_1}{E_2}=4$. When amplitude doubles, energy quadruples: $(2A)^2 = 4A^2$.

11. Which wave carries more energy if both have the same wavelength but Wave A has larger amplitude?

    Wave A. Larger amplitude means more energy when other factors are equal.

12. Identify the amplitude on a graph if the crest is at $+6\ \text{cm}$ and equilibrium is $0\ \text{cm}$.

    $A = 6\ \text{cm}$. Amplitude is the distance from equilibrium to the peak.

13. What is amplitude on a wave graph (displacement vs. position or time)?

    Maximum displacement from the equilibrium line. Amplitude measures how far the wave moves from its rest position.

14. Which wave carries more energy if both have the same frequency but Wave B has smaller amplitude?

    The other wave (the one with larger amplitude). The wave with larger amplitude carries more energy regardless of frequency.

15. What is the qualitative relationship between wave amplitude and energy carried?

    Greater amplitude means greater energy carried. Higher amplitude waves carry more energy due to greater particle displacement.

16. Find $\frac{E_1}{E_2}$ for $A_1=4\text{ mm}$ and $A_2=6\text{ mm}$ if $E\propto A^2$.

    $\frac{E_1}{E_2}=\frac{16}{36}=\frac{4}{9}$. Square each amplitude and divide: $\frac{4^2}{6^2} = \frac{16}{36} = \frac{4}{9}$.

17. What does the equilibrium line represent on a wave displacement graph?

    The rest position where displacement is $0$. It's the baseline where the medium has no displacement from rest.

18. Which graph feature should you compare first to decide which wave carries more energy?

    Amplitude (height from equilibrium to crest or trough). Amplitude directly determines energy, making it the primary comparison feature.

19. A graph shows Wave A with amplitude $2\ \text{cm}$ and Wave B with amplitude $8\ \text{cm}$. What is $\frac{E_B}{E_A}$?

    $\frac{E_B}{E_A} = 16$. Energy ratio is $(\frac{8}{2})^2 = 4^2 = 16$ using $E \propto A^2$.

20. If Wave 1 has $A_1 = 3A_2$, what is the energy ratio $\frac{E_1}{E_2}$ (same wave type)?

    $\frac{E_1}{E_2} = 9$. Since $E \propto A^2$, tripling amplitude gives $3^2 = 9$ times the energy.

21. Find the energy ratio $\frac{E_1}{E_2}$ if $A_1=3A_2$ and $E\propto A^2$.

    $\frac{E_1}{E_2}=9$. When amplitude triples, energy increases ninefold: $(3A)^2 = 9A^2$.

22. If a wave's amplitude doubles, by what factor does its energy change when $E\propto A^2$?

    Energy increases by a factor of $4$. Doubling amplitude quadruples energy since $E \propto A^2$.

23. State the relationship between wave energy and amplitude for many mechanical waves.

    Energy is proportional to amplitude squared: $E \propto A^2$. Doubling amplitude quadruples energy since energy depends on amplitude squared.

24. Choose the correct comparison: amplitudes $A_1=4\text{ mm}$ and $A_2=6\text{ mm}$; which has greater energy?

    Wave 2. $6\text{ mm} > 4\text{ mm}$, so Wave 2 has greater amplitude and energy.

25. Which option correctly describes how to find amplitude from a wave graph?

    Measure from equilibrium to a crest (or to a trough). Amplitude is always measured from the center line, not peak-to-peak.

26. What is the amplitude if a wave's crest-to-trough height is $14\ \text{cm}$?

    $A = 7\ \text{cm}$. Amplitude is half the crest-to-trough distance.

27. Identify the energy comparison if Wave X has amplitude $0\ \text{cm}$ on the graph.

    It carries $0$ energy in the wave (no oscillation). Zero amplitude means no oscillation, therefore no wave energy.

28. If a wave's amplitude is cut in half, by what factor does energy change when $E\propto A^2$?

    Energy becomes $\frac{1}{4}$ as large. Halving amplitude reduces energy to one-fourth: $(\frac{A}{2})^2 = \frac{A^2}{4}$.

29. Identify the amplitude on a graph where crest is at $+5\text{ mm}$ and equilibrium is $0\text{ mm}$.

    $5\text{ mm}$. Amplitude equals the distance from equilibrium to peak.

30. Find the amplitude if the maximum displacement shown is $+0.12\ \text{m}$ from equilibrium.

    $A = 0.12\ \text{m}$. The maximum displacement from equilibrium equals the amplitude.

31. Find the amplitude if the wave ranges from $-3\ \text{cm}$ to $+9\ \text{cm}$.

    $A = 6\ \text{cm}$. Find the midpoint: $\frac{-3 + 9}{2} = 3$, then amplitude is $9 - 3 = 6$ cm.

32. State the common proportionality between wave energy and amplitude for many waves.

    Energy is proportional to $A^2$. Energy increases with the square of amplitude for most wave types.

33. What is amplitude if the crest-to-trough height is $12\text{ cm}$ on a displacement graph?

    $6\text{ cm}$. Amplitude is half the total vertical distance between crest and trough.

34. Which option correctly compares energy for amplitudes $A_1 = 7\ \text{cm}$ and $A_2 = 1\ \text{cm}$?

    $\frac{E_1}{E_2} = 49$. Energy ratio is $(\frac{7}{1})^2 = 49$ using $E \propto A^2$.

35. Which wave carries more energy if two waves have the same type and frequency but different amplitudes?

    The wave with the larger amplitude. Energy increases with amplitude squared, so larger amplitude means more energy.

36. Two waves have amplitudes $4\ \text{cm}$ and $6\ \text{cm}$. What is $\frac{E_{6}}{E_{4}}$ if $E \propto A^2$?

    $\frac{E_{6}}{E_{4}} = \frac{36}{16} = \frac{9}{4}$. Energy ratio equals amplitude ratio squared: $(\frac{6}{4})^2 = \frac{9}{4}$.

37. What is the correct unit interpretation when amplitude is labeled in meters on a graph?

    Amplitude is a distance (displacement) measured in meters. Meters indicate the physical displacement of the wave medium.

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