AP Physics 2 Flashcards: Wave Interference And Standing Waves

What this deck covers

This deck focuses on Wave Interference And Standing Waves, giving you a quick way to review the definitions, rules, and examples that matter most for AP Physics 2.

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 is the speed of a wave with $\text{\textit{λ}} = 3 \text{ m}$, $f = 100 \text{ Hz}$?

Answer: Wave speed $v = 300 \text{ m/s}$.. Using $v = f\lambda = 100 \times 3 = 300$ m/s.

Flashcard 2: What is an antinode?

Answer: A point where the amplitude of a standing wave is maximum. Point of constructive interference in standing wave patterns.

Flashcard 3: What is the equation for wave speed?

Answer: $v = f\text{\textit{λ}}$, where $f$ is frequency, $\text{\textit{λ}}$ is wavelength. Fundamental relationship between wave properties.

Flashcard 4: Identify the condition for destructive interference.

Answer: Path difference is an odd multiple of $\frac{\text{\textit{λ}}}{2}$. Waves arrive out of phase when path difference is half-wavelengths.

Flashcard 5: If a wave has an amplitude $A$, what is its intensity proportional to?

Answer: Intensity is proportional to $A^2$. Wave energy is proportional to amplitude squared.

Flashcard 6: What determines the frequency of a standing wave in a string?

Answer: String length, tension, and mass per unit length. These parameters determine the fundamental frequency and harmonics.

Flashcard 7: State the formula for the fundamental frequency of a string.

Answer: $f_1 = \frac{v}{2L}$, where $v$ is wave speed, $L$ is length. The lowest frequency mode for a vibrating string.

Flashcard 8: What is a standing wave?

Answer: A wave that appears to be stationary, with nodes and antinodes. Formed by two waves traveling in opposite directions interfering.

Flashcard 9: Calculate the length of a string for a fundamental frequency of $440 \text{ Hz}$, $v = 330 \text{ m/s}$.

Answer: Length $L = 0.375 \text{ m}$. Using $L = \frac{v}{2f_1} = \frac{330}{2 \times 440} = 0.375$ m.

Flashcard 10: What is the phase shift for waves in antiphase?

Answer: Phase difference of $\text{\textit{π}}$ radians. Antiphase means waves are exactly out of phase by half cycle.

Flashcard 11: What is the formula for the nth harmonic frequency?

Answer: $f_n = n\frac{v}{2L}$, $n = 1, 2, 3, \text{...}$. Each harmonic is an integer multiple of the fundamental frequency.

Flashcard 12: What is the relationship between frequency and wavelength?

Answer: Inversely proportional: $f \text{\textit{λ}} = v$.. Higher frequency means shorter wavelength for constant wave speed.

Flashcard 13: State the relationship between wave speed and medium.

Answer: Wave speed depends on the medium's properties. Wave speed is independent of frequency for a given medium.

Flashcard 14: Calculate wave speed for $\text{\textit{λ}} = 5 \text{ m}$, $f = 50 \text{ Hz}$.

Answer: Wave speed $v = 250 \text{ m/s}$. Using $v = f\lambda = 50 \times 5 = 250$ m/s.

Flashcard 15: What is the phase difference for complete destructive interference?

Answer: Phase difference is $\text{\textit{π}}$ radians. Waves oscillate in perfect opposition.

Flashcard 16: Identify the condition for constructive interference.

Answer: Path difference is a multiple of the wavelength, $n \lambda$. Waves arrive in phase when path difference equals whole wavelengths.

Flashcard 17: What is a standing wave?

Answer: A wave that appears to be stationary, with nodes and antinodes. Formed by two waves traveling in opposite directions interfering.

Flashcard 18: Calculate the third harmonic for $L = 1 \text{ m}$, $v = 340 \text{ m/s}$.

Answer: Third harmonic $f_3 = 510 \text{ Hz}$. Using $f_3 = 3f_1 = 3 \cdot \frac{340}{2} = 510$ Hz.

Flashcard 19: Determine the beat frequency for $f_1 = 256 \text{ Hz}$, $f_2 = 260 \text{ Hz}$.

Answer: Beat frequency is $4 \text{ Hz}$. Using $f_{beat} = |256 - 260| = 4$ Hz.

Flashcard 20: Identify the condition for destructive interference.

Answer: Path difference is an odd multiple of $\frac{\text{\textit{λ}}}{2}$. Waves arrive out of phase when path difference is half-wavelengths.

Flashcard 21: Calculate the fundamental frequency for $L = 0.5 \text{ m}$, $v = 300 \text{ m/s}$.

Answer: $f_1 = 300 \text{ Hz}$. Using $f_1 = \frac{v}{2L} = \frac{300}{2 \times 0.5} = 300$ Hz.

Flashcard 22: What is the relationship between frequency and wavelength?

Answer: Inversely proportional: $f \text{\textit{λ}} = v$.. Higher frequency means shorter wavelength for constant wave speed.

Flashcard 23: Calculate the frequency of the second harmonic for $L = 2 \text{ m}$, $v = 340 \text{ m/s}$.

Answer: $f_2 = 170 \text{ Hz}$.. Second harmonic: $f_2 = 2f_1 = 2 \cdot \frac{340}{4} = 170$ Hz.

Flashcard 24: Identify the condition for constructive interference.

Answer: Path difference is a multiple of the wavelength, $n\text{\textit{λ}}$.. Waves arrive in phase when path difference equals whole wavelengths.

Flashcard 25: State the relationship between nodes and antinodes.

Answer: Nodes are points of no displacement; antinodes have maximum displacement. Nodes and antinodes are separated by $\frac{\lambda}{4}$.

Flashcard 26: Calculate the third harmonic for $L = 1 \text{ m}$, $v = 340 \text{ m/s}$.

Answer: Third harmonic $f_3 = 510 \text{ Hz}$. Using $f_3 = 3f_1 = 3 \cdot \frac{340}{2} = 510$ Hz.

Flashcard 27: State the relationship between wave speed and medium.

Answer: Wave speed depends on the medium's properties. Wave speed is independent of frequency for a given medium.

Flashcard 28: Calculate the frequency of the second harmonic for $L = 2 \text{ m}$, $v = 340 \text{ m/s}$.

Answer: $f_2 = 170 \text{ Hz}$.. Second harmonic: $f_2 = 2f_1 = 2 \cdot \frac{340}{4} = 170$ Hz.

Flashcard 29: Define constructive interference.

Answer: Occurs when wave amplitudes add to create a larger amplitude. Waves are in phase, causing amplification of the resultant wave.

Flashcard 30: If a wave has an amplitude $A$, what is its intensity proportional to?

Answer: Intensity is proportional to $A^2$. Wave energy is proportional to amplitude squared.

Flashcard 31: If two waves meet out of phase, what is the result?

Answer: Destructive interference. Out of phase waves interfere destructively, reducing amplitude.

Flashcard 32: What is the impact of damping on a standing wave?

Answer: Damping reduces wave amplitude over time. Energy dissipation causes gradual decay of oscillation amplitude.

Flashcard 33: What is the impact of damping on a standing wave?

Answer: Damping reduces wave amplitude over time. Energy dissipation causes gradual decay of oscillation amplitude.

Flashcard 34: Calculate the fundamental frequency for $L = 0.5 \text{ m}$, $v = 300 \text{ m/s}$.

Answer: $f_1 = 300 \text{ Hz}$. Using $f_1 = \frac{v}{2L} = \frac{300}{2 \times 0.5} = 300$ Hz.

Flashcard 35: Find the wavelength of a wave given $v = 340 \text{ m/s}$, $f = 170 \text{ Hz}$.

Answer: Wavelength $\text{\textit{λ}} = 2 \text{ m}$. Using $\lambda = \frac{v}{f} = \frac{340}{170} = 2$ m.

Flashcard 36: What is the phase difference for complete constructive interference?

Answer: Phase difference is $0$ or $2\text{\textit{π}}$ radians. Waves oscillate in perfect synchronization.

Flashcard 37: What is formed when two waves of the same frequency and amplitude meet in phase?

Answer: A resultant wave with doubled amplitude. Perfect constructive interference produces maximum possible amplitude.

Flashcard 38: What determines the frequency of a standing wave in a string?

Answer: String length, tension, and mass per unit length. These parameters determine the fundamental frequency and harmonics.

Flashcard 39: State the relationship between nodes and antinodes.

Answer: Nodes are points of no displacement; antinodes have maximum displacement. Nodes and antinodes are separated by $\frac{\lambda}{4}$.

Flashcard 40: What is the effect of tension on wave speed in a string?

Answer: Increased tension increases wave speed. Higher tension provides greater restoring force, increasing wave speed.

Flashcard 41: Identify the type of interference with a phase difference of $\frac{\text{\textit{π}}}{2}$.

Answer: Neither complete constructive nor destructive interference. Partial interference occurs with phase differences between 0 and $\pi$.

Flashcard 42: Calculate the length of a string for a fundamental frequency of $440 \text{ Hz}$, $v = 330 \text{ m/s}$.

Answer: Length $L = 0.375 \text{ m}$. Using $L = \frac{v}{2f_1} = \frac{330}{2 \times 440} = 0.375$ m.

Flashcard 43: What is the formula for the nth harmonic frequency?

Answer: $f_n = n\frac{v}{2L}$, $n = 1, 2, 3, \text{...}$. Each harmonic is an integer multiple of the fundamental frequency.

Flashcard 44: What is the phase difference for complete constructive interference?

Answer: Phase difference is $0$ or $2\text{\textit{π}}$ radians. Waves oscillate in perfect synchronization.

Flashcard 45: Identify the effect of boundary conditions on standing waves.

Answer: Nodes at fixed boundaries; antinodes at open boundaries. Boundary conditions determine the standing wave pattern.

Flashcard 46: State the formula for the fundamental frequency of a string.

Answer: $f_1 = \frac{v}{2L}$, where $v$ is wave speed, $L$ is length. The lowest frequency mode for a vibrating string.

Flashcard 47: If two waves meet out of phase, what is the result?

Answer: Destructive interference. Out of phase waves interfere destructively, reducing amplitude.

Flashcard 48: What is a node?

Answer: A point along a standing wave with zero amplitude. Point of destructive interference in standing wave patterns.

Flashcard 49: What is formed when two waves of the same frequency and amplitude meet in phase?

Answer: A resultant wave with doubled amplitude. Perfect constructive interference produces maximum possible amplitude.

Flashcard 50: Identify the effect of boundary conditions on standing waves.

Answer: Nodes at fixed boundaries; antinodes at open boundaries. Boundary conditions determine the standing wave pattern.

Flashcard 51: What is the equation for wave speed?

Answer: $v = f\text{\textit{λ}}$, where $f$ is frequency, $\text{\textit{λ}}$ is wavelength. Fundamental relationship between wave properties.

Flashcard 52: Determine the first overtone frequency for $f_1 = 220 \text{ Hz}$.

Answer: First overtone frequency is $440 \text{ Hz}$. First overtone is the second harmonic: $f_2 = 2f_1$.

Flashcard 53: Find the wavelength of a wave given $v = 340 \text{ m/s}$, $f = 170 \text{ Hz}$.

Answer: Wavelength $\text{\textit{λ}} = 2 \text{ m}$. Using $\lambda = \frac{v}{f} = \frac{340}{170} = 2$ m.

Flashcard 54: Identify the type of interference with a phase difference of $\frac{\text{\textit{π}}}{2}$.

Answer: Neither complete constructive nor destructive interference. Partial interference occurs with phase differences between 0 and $\pi$.

Flashcard 55: Define destructive interference.

Answer: Occurs when wave amplitudes cancel to create a smaller amplitude. Waves are out of phase, reducing the resultant amplitude.

Flashcard 56: What happens to wave speed if tension in a string is halved?

Answer: Wave speed decreases by factor of $\frac{1}{\text{\textit{√2}}}$. Wave speed is proportional to $\sqrt{T}$, so halving tension reduces speed.

Flashcard 57: What is the speed of a wave with $\text{\textit{λ}} = 3 \text{ m}$, $f = 100 \text{ Hz}$?

Answer: Wave speed $v = 300 \text{ m/s}$.. Using $v = f\lambda = 100 \times 3 = 300$ m/s.

Flashcard 58: Calculate wave speed for $\text{\textit{λ}} = 5 \text{ m}$, $f = 50 \text{ Hz}$.

Answer: Wave speed $v = 250 \text{ m/s}$. Using $v = f\lambda = 50 \times 5 = 250$ m/s.

Flashcard 59: Which physical quantity remains unchanged in standing waves?

Answer: The frequency of the wave remains unchanged. Standing waves maintain constant frequency as amplitude varies spatially.

Flashcard 60: How do you calculate beat frequency?

Answer: Beat frequency is $|f_1 - f_2|$, where $f_1$ and $f_2$ are frequencies. Beat frequency equals the absolute difference between interfering frequencies.

Flashcard 61: Determine the beat frequency for $f_1 = 256 \text{ Hz}$, $f_2 = 260 \text{ Hz}$.

Answer: Beat frequency is $4 \text{ Hz}$. Using $f_{beat} = |256 - 260| = 4$ Hz.

Flashcard 62: What is the effect of tension on wave speed in a string?

Answer: Increased tension increases wave speed. Higher tension provides greater restoring force, increasing wave speed.

Flashcard 63: How do you calculate beat frequency?

Answer: Beat frequency is $|f_1 - f_2|$, where $f_1$ and $f_2$ are frequencies. Beat frequency equals the absolute difference between interfering frequencies.

Flashcard 64: What is the phase difference for complete destructive interference?

Answer: Phase difference is $\text{\textit{π}}$ radians. Waves oscillate in perfect opposition.

Flashcard 65: What is the phase shift for waves in antiphase?

Answer: Phase difference of $\text{\textit{π}}$ radians. Antiphase means waves are exactly out of phase by half cycle.

Flashcard 66: Determine the first overtone frequency for $f_1 = 220 \text{ Hz}$.

Answer: First overtone frequency is $440 \text{ Hz}$. First overtone is the second harmonic: $f_2 = 2f_1$.

Flashcard 67: Which physical quantity remains unchanged in standing waves?

Answer: The frequency of the wave remains unchanged. Standing waves maintain constant frequency as amplitude varies spatially.

Flashcard 68: What happens to wave speed if tension in a string is halved?

Answer: Wave speed decreases by factor of $\frac{1}{\sqrt{2}}$. Wave speed is proportional to $\sqrt{T}$, so halving tension reduces speed.

Flashcard 69: What is the principle of superposition?

Answer: The net displacement is the sum of individual displacements. This describes wave superposition where effects combine algebraically.

Flashcard 70: What is the formula for intensity of a wave?

Answer: $I = \frac{P}{A}$, where $P$ is power, $A$ is the area. Intensity measures energy flow per unit area per unit time.