Compare Wave Energy - Middle School Physical Science
Card 1 of 25
Which graph feature should you compare first to decide which wave carries more energy?
Which graph feature should you compare first to decide which wave carries more energy?
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Amplitude (height from equilibrium to crest or trough). Amplitude directly determines energy, making it the primary comparison feature.
Amplitude (height from equilibrium to crest or trough). Amplitude directly determines energy, making it the primary comparison feature.
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What is amplitude on a wave graph (displacement vs. position or time)?
What is amplitude on a wave graph (displacement vs. position or time)?
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Maximum displacement from the equilibrium line. Amplitude measures how far the wave moves from its rest position.
Maximum displacement from the equilibrium line. Amplitude measures how far the wave moves from its rest position.
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What is amplitude if the crest-to-trough height is $12\text{ cm}$ on a displacement graph?
What is amplitude if the crest-to-trough height is $12\text{ cm}$ on a displacement graph?
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$6\text{ cm}$. Amplitude is half the total vertical distance between crest and trough.
$6\text{ cm}$. Amplitude is half the total vertical distance between crest and trough.
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Which wave carries more energy if both have the same wavelength but Wave A has larger amplitude?
Which wave carries more energy if both have the same wavelength but Wave A has larger amplitude?
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Wave A. Larger amplitude means more energy when other factors are equal.
Wave A. Larger amplitude means more energy when other factors are equal.
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Which wave carries more energy if both have the same frequency but Wave B has smaller amplitude?
Which wave carries more energy if both have the same frequency but Wave B has smaller amplitude?
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The other wave (the one with larger amplitude). The wave with larger amplitude carries more energy regardless of frequency.
The other wave (the one with larger amplitude). The wave with larger amplitude carries more energy regardless of frequency.
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Identify the amplitude on a graph where trough is at $-8\text{ mm}$ and equilibrium is $0\text{ mm}$.
Identify the amplitude on a graph where trough is at $-8\text{ mm}$ and equilibrium is $0\text{ mm}$.
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$8\text{ mm}$. Amplitude equals the distance from equilibrium to trough (absolute value).
$8\text{ mm}$. Amplitude equals the distance from equilibrium to trough (absolute value).
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Identify the amplitude on a graph where crest is at $+5\text{ mm}$ and equilibrium is $0\text{ mm}$.
Identify the amplitude on a graph where crest is at $+5\text{ mm}$ and equilibrium is $0\text{ mm}$.
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$5\text{ mm}$. Amplitude equals the distance from equilibrium to peak.
$5\text{ mm}$. Amplitude equals the distance from equilibrium to peak.
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If a wave’s amplitude is cut in half, by what factor does energy change when $E\propto A^2$?
If a wave’s amplitude is cut in half, by what factor does energy change when $E\propto A^2$?
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Energy becomes $\frac{1}{4}$ as large. Halving amplitude reduces energy to one-fourth: $(\frac{A}{2})^2 = \frac{A^2}{4}$.
Energy becomes $\frac{1}{4}$ as large. Halving amplitude reduces energy to one-fourth: $(\frac{A}{2})^2 = \frac{A^2}{4}$.
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If a wave’s amplitude doubles, by what factor does its energy change when $E\propto A^2$?
If a wave’s amplitude doubles, by what factor does its energy change when $E\propto A^2$?
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Energy increases by a factor of $4$. Doubling amplitude quadruples energy since $E \propto A^2$.
Energy increases by a factor of $4$. Doubling amplitude quadruples energy since $E \propto A^2$.
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Find the energy ratio $\frac{E_1}{E_2}$ if $A_1=3A_2$ and $E\propto A^2$.
Find the energy ratio $\frac{E_1}{E_2}$ if $A_1=3A_2$ and $E\propto A^2$.
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$\frac{E_1}{E_2}=9$. When amplitude triples, energy increases ninefold: $(3A)^2 = 9A^2$.
$\frac{E_1}{E_2}=9$. When amplitude triples, energy increases ninefold: $(3A)^2 = 9A^2$.
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What is the correct unit interpretation when amplitude is labeled in meters on a graph?
What is the correct unit interpretation when amplitude is labeled in meters on a graph?
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Amplitude is a distance (displacement) measured in meters. Meters indicate the physical displacement of the wave medium.
Amplitude is a distance (displacement) measured in meters. Meters indicate the physical displacement of the wave medium.
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Choose the correct comparison: amplitudes $A_1=4\text{ mm}$ and $A_2=6\text{ mm}$; which has greater energy?
Choose the correct comparison: amplitudes $A_1=4\text{ mm}$ and $A_2=6\text{ mm}$; which has greater energy?
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Wave 2. $6\text{ mm} > 4\text{ mm}$, so Wave 2 has greater amplitude and energy.
Wave 2. $6\text{ mm} > 4\text{ mm}$, so Wave 2 has greater amplitude and energy.
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Find $\frac{E_1}{E_2}$ for $A_1=4\text{ mm}$ and $A_2=6\text{ mm}$ if $E\propto A^2$.
Find $\frac{E_1}{E_2}$ for $A_1=4\text{ mm}$ and $A_2=6\text{ mm}$ if $E\propto A^2$.
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$\frac{E_1}{E_2}=\frac{16}{36}=\frac{4}{9}$. Square each amplitude and divide: $\frac{4^2}{6^2} = \frac{16}{36} = \frac{4}{9}$.
$\frac{E_1}{E_2}=\frac{16}{36}=\frac{4}{9}$. Square each amplitude and divide: $\frac{4^2}{6^2} = \frac{16}{36} = \frac{4}{9}$.
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Identify the error: “Amplitude equals the distance from crest to trough.” What is the correction?
Identify the error: “Amplitude equals the distance from crest to trough.” What is the correction?
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Amplitude is half the crest-to-trough distance. Crest-to-trough is the full wave height; amplitude is only half that distance.
Amplitude is half the crest-to-trough distance. Crest-to-trough is the full wave height; amplitude is only half that distance.
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Which wave carries more energy if Wave 1 has amplitude $2\text{ cm}$ and Wave 2 has amplitude $1\text{ cm}$?
Which wave carries more energy if Wave 1 has amplitude $2\text{ cm}$ and Wave 2 has amplitude $1\text{ cm}$?
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Wave 1. Wave 1 has twice the amplitude, so it carries more energy.
Wave 1. Wave 1 has twice the amplitude, so it carries more energy.
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State the common proportionality between wave energy and amplitude for many waves.
State the common proportionality between wave energy and amplitude for many waves.
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Energy is proportional to $A^2$. Energy increases with the square of amplitude for most wave types.
Energy is proportional to $A^2$. Energy increases with the square of amplitude for most wave types.
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What is the qualitative relationship between wave amplitude and energy carried?
What is the qualitative relationship between wave amplitude and energy carried?
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Greater amplitude means greater energy carried. Higher amplitude waves carry more energy due to greater particle displacement.
Greater amplitude means greater energy carried. Higher amplitude waves carry more energy due to greater particle displacement.
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Find the energy ratio $\frac{E_1}{E_2}$ if amplitudes are $A_1=2A_2$ and $E\propto A^2$.
Find the energy ratio $\frac{E_1}{E_2}$ if amplitudes are $A_1=2A_2$ and $E\propto A^2$.
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$\frac{E_1}{E_2}=4$. When amplitude doubles, energy quadruples: $(2A)^2 = 4A^2$.
$\frac{E_1}{E_2}=4$. When amplitude doubles, energy quadruples: $(2A)^2 = 4A^2$.
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If Wave 1 has $A_1 = \frac{1}{2}A_2$, what is the energy ratio $\frac{E_1}{E_2}$?
If Wave 1 has $A_1 = \frac{1}{2}A_2$, what is the energy ratio $\frac{E_1}{E_2}$?
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$\frac{E_1}{E_2} = \frac{1}{4}$. Halving amplitude gives $(\frac{1}{2})^2 = \frac{1}{4}$ the energy.
$\frac{E_1}{E_2} = \frac{1}{4}$. Halving amplitude gives $(\frac{1}{2})^2 = \frac{1}{4}$ the energy.
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Two waves have amplitudes $4\ \text{cm}$ and $6\ \text{cm}$. What is $\frac{E_{6}}{E_{4}}$ if $E \propto A^2$?
Two waves have amplitudes $4\ \text{cm}$ and $6\ \text{cm}$. What is $\frac{E_{6}}{E_{4}}$ if $E \propto A^2$?
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$\frac{E_{6}}{E_{4}} = \frac{36}{16} = \frac{9}{4}$. Energy ratio equals amplitude ratio squared: $(\frac{6}{4})^2 = \frac{9}{4}$.
$\frac{E_{6}}{E_{4}} = \frac{36}{16} = \frac{9}{4}$. Energy ratio equals amplitude ratio squared: $(\frac{6}{4})^2 = \frac{9}{4}$.
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Two waves have amplitudes $5\ \text{mm}$ and $10\ \text{mm}$. Which carries more energy (same wave type)?
Two waves have amplitudes $5\ \text{mm}$ and $10\ \text{mm}$. Which carries more energy (same wave type)?
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The $10\ \text{mm}$ amplitude wave. Double amplitude means quadruple energy since $E \propto A^2$.
The $10\ \text{mm}$ amplitude wave. Double amplitude means quadruple energy since $E \propto A^2$.
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Identify which graph feature is most important for comparing energy when wave type is the same.
Identify which graph feature is most important for comparing energy when wave type is the same.
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Amplitude (height from equilibrium). Energy depends on amplitude squared, making it the key comparison factor.
Amplitude (height from equilibrium). Energy depends on amplitude squared, making it the key comparison factor.
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Find the amplitude if the maximum displacement shown is $+0.12\ \text{m}$ from equilibrium.
Find the amplitude if the maximum displacement shown is $+0.12\ \text{m}$ from equilibrium.
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$A = 0.12\ \text{m}$. The maximum displacement from equilibrium equals the amplitude.
$A = 0.12\ \text{m}$. The maximum displacement from equilibrium equals the amplitude.
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Find the amplitude if the wave ranges from $-3\ \text{cm}$ to $+9\ \text{cm}$.
Find the amplitude if the wave ranges from $-3\ \text{cm}$ to $+9\ \text{cm}$.
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$A = 6\ \text{cm}$. Find the midpoint: $\frac{-3 + 9}{2} = 3$, then amplitude is $9 - 3 = 6$ cm.
$A = 6\ \text{cm}$. Find the midpoint: $\frac{-3 + 9}{2} = 3$, then amplitude is $9 - 3 = 6$ cm.
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Which option correctly compares energy for amplitudes $A_1 = 7\ \text{cm}$ and $A_2 = 1\ \text{cm}$?
Which option correctly compares energy for amplitudes $A_1 = 7\ \text{cm}$ and $A_2 = 1\ \text{cm}$?
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$\frac{E_1}{E_2} = 49$. Energy ratio is $(\frac{7}{1})^2 = 49$ using $E \propto A^2$.
$\frac{E_1}{E_2} = 49$. Energy ratio is $(\frac{7}{1})^2 = 49$ using $E \propto A^2$.
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