Podcast
Questions and Answers
If the frequency of a wave is doubled while its velocity remains constant, what happens to its wavelength?
If the frequency of a wave is doubled while its velocity remains constant, what happens to its wavelength?
- It remains the same.
- It is doubled.
- It is quadrupled.
- It is halved. (correct)
Which of the following best describes a longitudinal wave?
Which of the following best describes a longitudinal wave?
- A wave in which the particle displacement is perpendicular to the direction of propagation.
- A wave in which the particle displacement is parallel to the direction of propagation. (correct)
- A wave that requires a medium to travel.
- A wave that transfers energy through a vacuum.
What aspect of a sound wave is most directly related to its perceived loudness?
What aspect of a sound wave is most directly related to its perceived loudness?
- Amplitude (correct)
- Speed
- Frequency
- Wavelength
A car is moving towards an observer. How does the perceived frequency of the sound of the car's horn change, and what is this phenomenon called?
A car is moving towards an observer. How does the perceived frequency of the sound of the car's horn change, and what is this phenomenon called?
What phenomenon explains why a straw appears bent when placed in a glass of water?
What phenomenon explains why a straw appears bent when placed in a glass of water?
Which of the following correctly relates voltage, current, and resistance in a circuit, according to Ohm's Law?
Which of the following correctly relates voltage, current, and resistance in a circuit, according to Ohm's Law?
When light strikes a green leaf, why does the leaf appear green?
When light strikes a green leaf, why does the leaf appear green?
In a series circuit with multiple resistors, what quantity remains the same across each resistor?
In a series circuit with multiple resistors, what quantity remains the same across each resistor?
Which of the following applications relies primarily on the phenomenon of reflection?
Which of the following applications relies primarily on the phenomenon of reflection?
How does increasing the resistance in a circuit affect the current, assuming the voltage remains constant?
How does increasing the resistance in a circuit affect the current, assuming the voltage remains constant?
What kind of wave is a sound wave?
What kind of wave is a sound wave?
Which property of a wave is defined as the distance between two consecutive crests or troughs?
Which property of a wave is defined as the distance between two consecutive crests or troughs?
How does the eye perceive different colors of light?
How does the eye perceive different colors of light?
What happens to the overall resistance in a parallel circuit when you add more resistors?
What happens to the overall resistance in a parallel circuit when you add more resistors?
How does the speed of light change when it moves from air into glass?
How does the speed of light change when it moves from air into glass?
What is the relationship between pitch and frequency of a sound wave?
What is the relationship between pitch and frequency of a sound wave?
What is the primary function of circuit diagrams?
What is the primary function of circuit diagrams?
Which of the following correctly describes the relationship between voltage and current in a purely resistive circuit, given a constant resistance?
Which of the following correctly describes the relationship between voltage and current in a purely resistive circuit, given a constant resistance?
In the context of wave properties, what does 'amplitude' refer to?
In the context of wave properties, what does 'amplitude' refer to?
What is the role of the ear in responding to sound waves?
What is the role of the ear in responding to sound waves?
Flashcards
What are transverse waves?
What are transverse waves?
Waves in which the displacement is perpendicular to the direction of propagation.
What are longitudinal waves?
What are longitudinal waves?
Waves in which the displacement is parallel to the direction of propagation.
What is wavelength?
What is wavelength?
The distance between two successive crests or troughs of a wave.
What is frequency?
What is frequency?
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What is amplitude?
What is amplitude?
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What is the wave equation?
What is the wave equation?
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What is pitch?
What is pitch?
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What is loudness?
What is loudness?
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What is the Doppler effect?
What is the Doppler effect?
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What is absorption?
What is absorption?
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What is reflection?
What is reflection?
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What is refraction?
What is refraction?
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What is a series circuit?
What is a series circuit?
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What is a parallel circuit?
What is a parallel circuit?
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What is voltage?
What is voltage?
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What is current?
What is current?
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What is a circuit diagram?
What is a circuit diagram?
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What is Ohm's Law?
What is Ohm's Law?
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Study Notes
- Game theory involves mathematical models of strategic interactions among rational agents.
- It is applicable in economics, political science, biology and computer science.
Key Game Theory Concepts
- Players are the decision-making individuals or entities.
- Strategies are the actions available to each player.
- Payoffs are the outcomes or rewards for each player based on chosen strategies.
- Rationality is the assumption that players maximize their payoffs.
Normal-Form Games
- Normal form games specify players, strategies, and payoffs.
- They are typically represented by a payoff matrix.
Prisoner's Dilemma
- Two suspects are arrested and cannot communicate, offered deals by the police.
- If one confesses and the other does not, the confessor goes free, and the other gets 10 years in prison.
- If both confess, they each get 5 years in prison, and if neither confesses, they each get 1 year in prison.
Prisoner's Dilemma Payoff Matrix
| Suspect B Confesses | Suspect B Stays Silent | |
|---|---|---|
| Suspect A Confesses | (-5, -5) | (0, -10) |
| Suspect A Stays Silent | (-10, 0) | (-1, -1) |
- The numbers in each cell represent the payoffs (years in prison) for Suspect A and Suspect B, respectively.
Dominant Strategies
- Yield the highest payoff for a player regardless of other players' strategies.
- In the Prisoner's Dilemma, confessing is a dominant strategy for both suspects.
- If Suspect B confesses, Suspect A is better off confessing (-5 years vs. -10 years).
- If Suspect B stays silent, Suspect A is better off confessing (0 years vs. -1 year).
Nash Equilibrium
- A set of strategies where no player can improve their payoff by unilaterally changing their strategy.
- In the Prisoner's Dilemma, the Nash Equilibrium is for both suspects to confess.
- Given that Suspect B confesses, Suspect A cannot improve their payoff by staying silent.
- Given that Suspect A confesses, Suspect B cannot improve their payoff by staying silent.
Algorithmic Game Theory (AGT)
- Combines game theory and computer science .
- Focuses on solving game-theoretic problems.
- Analyzing the computational complexity of game-theoretic solution concepts.
- Understanding the impact of strategic behavior on algorithm performance
Key Areas of AGT
- Mechanism Design: Designing rules for games to achieve desired outcomes, even when players act strategically.
- Social Choice Theory: Designing voting systems and other mechanisms for collective decision-making.
- Equilibrium Computation: Developing algorithms for finding Nash Equilibria and other solution concepts in large games.
- Price of Anarchy: Quantifying the inefficiency that results from selfish behavior in systems.
Price of Anarchy
- Measures the degradation of a system's performance due to selfish behavior, defined as the ratio of worst-case social welfare in a Nash Equilibrium to the optimal social welfare. $$ PoA = \frac{\text{Worst-case Social Welfare in Nash Equilibrium}}{\text{Optimal Social Welfare}} $$
- Traffic routing is an example.
- The selfish outcome can be worse than the optimal outcome.
AGT Applications
- Applicable in internet economics, online advertising, social networks, and cloud computing.
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