Physics Flashcards: Analyze Wave Amplitude And Energy

What this deck covers

This deck focuses on Analyze Wave Amplitude And Energy, giving you a quick way to review the definitions, rules, and examples that matter most for Physics.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What happens to wave energy if amplitude increases by $10\%$ (from $A$ to $1.10A$)?

Answer: Energy becomes $1.21E$. $(1.10A)^2 = 1.21A^2$, so energy increases to $1.21E$.

Flashcard 2: State the formula relating energy to amplitude when the proportionality constant is $k$.

Answer: $E = kA^2$. Where $k$ is a constant that depends on the wave type and medium.

Flashcard 3: If intensity decreases from $I$ to $\frac{1}{16}I$, what happens to amplitude?

Answer: Amplitude becomes $\frac{1}{4}A$. If $I_2 = \frac{1}{16}I_1$, then $(\frac{A_2}{A_1})^2 = \frac{1}{16}$, so $A_2 = \frac{1}{4}A_1$.

Flashcard 4: State the intensity-amplitude relationship for a wave in a given medium (constant speed).

Answer: $I \propto A^2$. Intensity is proportional to amplitude squared in a uniform medium.

Flashcard 5: What amplitude factor is needed to make a wave's energy increase by a factor of $16$?

Answer: Amplitude must increase by a factor of $4$. Since $E \propto A^2$, need $A^2 = 16$, so $A$ increases by $\sqrt{16} = 4$.

Flashcard 6: Which quantity depends on amplitude squared: frequency or intensity (in the same medium)?

Answer: Intensity. Frequency depends on source, not amplitude; intensity varies with $A^2$.

Flashcard 7: If intensity decreases to
frac{1}{4} of its original value, what happens to amplitude?

Answer: Amplitude decreases to
frac{1}{2} of the original. Since $I \propto A^2$ and $\frac{1}{4} = (\frac{1}{2})^2$, amplitude becomes $\frac{1}{2}$.

Flashcard 8: State the formula for the energy ratio of two identical waves with amplitudes $A_1$ and $A_2$.

Answer: $\frac{E_2}{E_1}=\left(\frac{A_2}{A_1}\right)^2$. Ratio of energies equals the square of the amplitude ratio.

Flashcard 9: If wave energy increases by a factor of $16$, what is the amplitude ratio $\frac{A_2}{A_1}$?

Answer: $\frac{A_2}{A_1}=4$. If $E_2 = 16E_1$, then $(\frac{A_2}{A_1})^2 = 16$, so $\frac{A_2}{A_1} = 4$.

Flashcard 10: Which graph best represents $E$ versus $A$ when $E \propto A^2$?

Answer: An upward-opening parabola through the origin. The function $E = kA^2$ is a parabola passing through $(0,0)$.

Flashcard 11: If a wave's amplitude is halved, by what factor does its energy change (assuming $E \propto A^2$)?

Answer: Energy becomes
frac{1}{4} of the original. Since $E \propto A^2$, halving $A$ gives $(\frac{1}{2})^2 = \frac{1}{4}$ the energy.

Flashcard 12: If intensity increases from $I$ to $9I$, what happens to amplitude?

Answer: Amplitude becomes $3A$. If $I_2 = 9I_1$, then $(\frac{A_2}{A_1})^2 = 9$, so $A_2 = 3A_1$.

Flashcard 13: Identify the correct equation for the intensity ratio of two waves with amplitudes $A_1$ and $A_2$.

Answer: $\frac{I_2}{I_1} = \left(\frac{A_2}{A_1}\right)^2$. Ratio of intensities equals the square of the amplitude ratio.

Flashcard 14: If amplitude increases by a factor of $5$, by what factor does intensity change (assuming $I \propto A^2$)?

Answer: Intensity increases by a factor of $25$. Since $I \propto A^2$, a 5-fold amplitude increase gives $5^2 = 25$ times intensity.

Flashcard 15: If intensity increases by a factor of $49$, by what factor did amplitude change (assuming $I \propto A^2$)?

Answer: Amplitude increased by a factor of $7$. Since $I \propto A^2$ and $49 = 7^2$, amplitude increased by $\sqrt{49} = 7$.

Flashcard 16: What relationship between wave amplitude $A$ and energy $E$ is typically used for mechanical waves?

Answer: $E \propto A^2$. Energy is proportional to the square of amplitude for mechanical waves.

Flashcard 17: For a string wave, if amplitude doubles while $\mu$, $\omega$, and $v$ stay constant, what happens to $P_{\text{avg}}$?

Answer: $P_{\text{avg}}$ becomes $4$ times larger. Power is proportional to $A^2$, so doubling $A$ quadruples power.

Flashcard 18: If $\frac{I_2}{I_1} = 0.01$, what is $\frac{A_2}{A_1}$ (same wave type and medium)?

Answer: $\frac{A_2}{A_1} = 0.1$. Since $\frac{I_2}{I_1} = (\frac{A_2}{A_1})^2 = 0.01$, so $\frac{A_2}{A_1} = \sqrt{0.01} = 0.1$.

Flashcard 19: Which graph best represents $E$ versus amplitude $A$ when $E \propto A^2$?

Answer: An upward-opening parabola through $(0,0)$. The quadratic relationship $E \propto A^2$ creates a parabola starting at origin.

Flashcard 20: If a wave's amplitude is halved from $A$ to $\frac{1}{2}A$, what happens to its energy?

Answer: Energy becomes $\frac{1}{4}E$. Halving amplitude gives $(\frac{1}{2}A)^2 = \frac{1}{4}A^2 = \frac{1}{4}E$.

Flashcard 21: If a wave's amplitude triples from $A$ to $3A$, what happens to its energy?

Answer: Energy becomes $9E$. Since $E \propto A^2$, tripling amplitude gives $(3A)^2 = 9A^2 = 9E$.

Flashcard 22: For a string wave, if frequency doubles (so $\omega$ doubles) while $A$, $\mu$, and $v$ stay constant, what happens to $P_{\text{avg}}$?

Answer: $P_{\text{avg}}$ becomes $4$ times larger. Power is proportional to $\omega^2$, so doubling $\omega$ quadruples power.

Flashcard 23: If a wave's amplitude doubles from $A$ to $2A$, what happens to its energy?

Answer: Energy becomes $4E$. Since $E \propto A^2$, doubling amplitude quadruples energy: $(2A)^2 = 4A^2$.

Flashcard 24: What is the average power on a string in terms of amplitude $A$, angular frequency $\omega$, and wave speed $v$?

Answer: $P_{\text{avg}}=\frac{1}{2}\mu \omega^2 A^2 v$. Power depends on $A^2$ and includes wave properties $\mu$, $\omega$, and $v$.

Flashcard 25: If a wave's amplitude doubles, by what factor does its energy change (assuming $E \propto A^2$)?

Answer: Energy increases by a factor of $4$. Since $E \propto A^2$, doubling $A$ gives $2^2 = 4$ times the energy.

Flashcard 26: If amplitude changes from $2\ \text{cm}$ to $6\ \text{cm}$, by what factor does energy change (assuming $E \propto A^2$)?

Answer: Energy increases by a factor of $9$. Amplitude triples ($\frac{6}{2} = 3$), so energy increases by $3^2 = 9$.

Flashcard 27: What happens to wave energy if amplitude decreases by $20\%$ (from $A$ to $0.80A$)?

Answer: Energy becomes $0.64E$. $(0.80A)^2 = 0.64A^2$, so energy decreases to $0.64E$.

Flashcard 28: If $A_2 = 3A_1$, what is $\frac{I_2}{I_1}$ for the same type of wave in the same medium?

Answer: $\frac{I_2}{I_1} = 9$. Using $\frac{I_2}{I_1} = (\frac{A_2}{A_1})^2 = (\frac{3A_1}{A_1})^2 = 3^2 = 9$.

Flashcard 29: What is the energy of a simple harmonic oscillator in terms of amplitude $A$ and spring constant $k$?

Answer: $E=\frac{1}{2}kA^2$. Total mechanical energy equals maximum potential energy at amplitude $A$.

Flashcard 30: What amplitude factor is needed to increase wave energy by a factor of $25$?

Answer: Amplitude must be multiplied by $5$. To get $E_2 = 25E_1$, need $(\frac{A_2}{A_1})^2 = 25$, so $\frac{A_2}{A_1} = 5$.

Flashcard 31: State the formula relating intensity to amplitude when the proportionality constant is $c$.

Answer: $I = cA^2$. Where $c$ depends on wave properties and medium characteristics.

Flashcard 32: What is the general relationship between wave energy and amplitude for many waves?

Answer: Energy is proportional to amplitude squared: $E \propto A^2$. Doubling amplitude quadruples energy due to the squared relationship.

Flashcard 33: For a mechanical wave, what does a larger amplitude indicate about energy transferred per unit time?

Answer: More energy transferred per unit time (greater power). Power is energy per time; larger amplitude waves carry more energy.

Flashcard 34: If the amplitude of a mass-spring oscillator changes from $A$ to $0.30A$, what happens to its total energy?

Answer: Energy becomes $0.09E$. $(0.30A)^2 = 0.09A^2$, so energy becomes $0.09E$.

Flashcard 35: What amplitude factor is needed to make a wave's energy decrease to
frac{1}{9} of its original value?

Answer: Amplitude must decrease by a factor of $3$. Since $E \propto A^2$, need $A^2 = \frac{1}{9}$, so $A$ decreases by $\sqrt{9} = 3$.

Flashcard 36: State the intensity ratio formula for two waves with amplitudes $A_1$ and $A_2$ in the same medium.

Answer: $\frac{I_2}{I_1}=\left(\frac{A_2}{A_1}\right)^2$. Intensity ratio equals the square of the amplitude ratio.

Flashcard 37: State the relationship between intensity and amplitude for a wave in a given medium.

Answer: Intensity is proportional to amplitude squared: $I \propto A^2$. Same squared relationship as energy since intensity is energy per unit area per time.

Flashcard 38: If a wave's amplitude is tripled, by what factor does its energy change (assuming $E \propto A^2$)?

Answer: Energy increases by a factor of $9$. Since $E \propto A^2$, tripling $A$ gives $3^2 = 9$ times the energy.

Flashcard 39: If energy changes from $E_1$ to $4E_1$, what is the new amplitude in terms of $A_1$ (assuming $E \propto A^2$)?

Answer: New amplitude is $2A_1$. Since $E \propto A^2$ and energy quadruples, $A$ doubles: $\sqrt{4} = 2$.

Flashcard 40: If wave energy decreases to $\frac{1}{9}$ of its original value, what is the new amplitude ratio $\frac{A_2}{A_1}$?

Answer: $\frac{A_2}{A_1}=\frac{1}{3}$. If $E_2 = \frac{1}{9}E_1$, then $(\frac{A_2}{A_1})^2 = \frac{1}{9}$, so $\frac{A_2}{A_1} = \frac{1}{3}$.