2019 AP Physics 1 Solutions Free Response #5

Allen Tsao The STEM Coach
9 May 201903:18
EducationalLearning
32 Likes 10 Comments

TLDRIn this educational video, Allen from Bothell STEM guides viewers through solving a 2019 AP Physics 1 free response question. The focus is on calculating the fundamental frequency of a vibrating air column in a tube, initially open at both ends, then with one end closed. The explanation involves understanding wave properties, such as wavelength and velocity, and applying them to determine the tube's length and the new frequency when conditions change. A graph of air molecule speed as a function of position within the tube is also discussed, illustrating the sinusoidal pattern of particle velocity.

Takeaways
  • πŸ“š The video is a lecture by Allen from Bothell STEM, focusing on the 2019 AP Physics 1 free response question 5.
  • 🎡 The subject matter involves a tuning fork vibrating at 512 Hertz and a tube that resonates at its fundamental frequency.
  • πŸ“ The tube's length (L) is calculated using the formula L = V / (2F), where V is the speed of sound and F is the frequency.
  • πŸ”’ The speed of sound (V) is given as 340 m/s, and when divided by sqrt(2), the length of the tube is found to be 0.332 meters.
  • πŸ“‰ The video discusses sketching a graph of the maximum speed of air molecules as a function of position within the tube, showing a sinusoidal pattern with zero velocity at L/2.
  • 🌐 The amplitude of air molecule velocity is related to the energy, which is proportional to the square of the velocity.
  • πŸ”„ When one end of the tube is closed, the fundamental frequency changes, and the wavelength (Ξ») becomes four times the length of the tube.
  • πŸ”’ The new fundamental frequency is calculated using the formula F = V / (4L), resulting in 750 Hz for the closed tube scenario.
  • πŸ“Š The video emphasizes the importance of understanding wave properties, such as nodes and antinodes, in the context of resonating air columns.
  • 🎼 The lecture aims to help students visualize and calculate wave behavior in different configurations of air columns within a tube.
  • πŸ“š The content is educational, providing a step-by-step explanation of how to approach physics problems involving wave resonance in tubes.
Q & A

  • What is the context of the video script provided?

    -The video script is a lecture by Allen from Bothell STEM, discussing the 2019 AP Physics 1 free response question 5, which involves the calculation of the fundamental frequency of a vibrating air column in a tube.

  • What is the initial frequency of the tuning fork mentioned in the script?

    -The tuning fork is vibrating at a frequency of 512 Hertz.

  • What is the relationship between the length of the tube (L) and the wavelength (lambda) when the tube is open at both ends?

    -In the case of a tube open at both ends, the relationship is lambda equals 2L, meaning the wavelength is twice the length of the tube.

  • How is the velocity of sound (V) related to the frequency (F) and the wavelength (lambda)?

    -The velocity of sound is related to frequency and wavelength by the formula V = lambda * F.

  • What is the formula to calculate the length of the tube (L) when the tube is open at both ends?

    -The formula to calculate L is L = lambda / 2, which can also be expressed as L = V / (2F), where V is the velocity of sound.

  • What is the calculated length of the tube when the air is resonating at its fundamental frequency?

    -The calculated length of the tube is 0.332 meters, obtained by dividing the velocity of sound (340 m/s) by the frequency (512 Hz) and then by 2.

  • What is the task when the tube is sketched with the maximum speed of air molecules as a function of position X?

    -The task is to sketch a graph that represents the maximum speed of air molecules oscillating in the tube, which should resemble a sinusoidal wave with maximum speed at the ends and zero speed at the midpoint.

  • What happens to the tube when the right end is kept shut?

    -When the right end of the tube is kept shut, the fundamental frequency changes, and the wavelength becomes four times the length of the tube (lambda = 4L).

  • How is the new fundamental frequency calculated when the right end of the tube is kept shut?

    -The new fundamental frequency is calculated using the formula F = V / (4L), where V is the velocity of sound and L is the length of the tube.

  • What is the new fundamental frequency when the right end of the tube is kept shut?

    -The new fundamental frequency is 750 Hertz, calculated by dividing the velocity of sound (340 m/s) by four times the length of the tube (4 * 0.332 m).

  • What is the significance of the velocity being maximum at the ends of the tube and zero at the midpoint?

    -The significance is that this pattern reflects the standing wave pattern in the tube, where the ends are antinodes (points of maximum displacement) and the midpoint is a node (a point of no displacement).

Outlines
00:00
πŸ”¬ Physics Problem: Calculating Tube Length and Resonance

In this paragraph, Allen from Bothell STEM Coach discusses a problem from the 2019 AP Physics 1 exam, specifically question 5. The scenario involves a tuning fork vibrating at 512 Hz and a tube open at both ends, which resonates at its fundamental frequency. The goal is to calculate the length of the tube (L) using the given parameters, such as the speed of sound (V) and the frequency (F). Allen explains that the fundamental frequency's wavelength (Ξ») is twice the length of the tube when open at both ends. He then uses the formula Ξ» = V/F to find L, resulting in approximately 0.332 meters. The paragraph also includes a brief mention of sketching a graph to represent the maximum speed of air molecules as a function of position within the tube, suggesting a sinusoidal pattern with maximum velocity at the ends and zero at the midpoint.

Mindmap
Keywords
πŸ’‘AP Physics 1
AP Physics 1 is a college-level course and exam offered by the College Board. It covers foundational concepts in physics, including mechanics, energy, and sound. In the video, the script discusses the 2019 AP Physics 1 free response questions, indicating the educational context and the specific subject matter being addressed.
πŸ’‘Free Response Questions
Free response questions are a type of assessment in the AP exams that require students to provide detailed answers, often in essay format, to demonstrate their understanding of the material. The script mentions looking at question 5, which implies a focus on a specific problem that requires in-depth analysis.
πŸ’‘Fundamental Frequency
The fundamental frequency is the lowest frequency of a periodic waveform, which in the context of sound, is the lowest pitch that can be produced by a musical instrument or a vibrating body. In the script, the fundamental frequency is discussed in relation to the resonance of air in a tube, which is a key concept in understanding wave behavior.
πŸ’‘Vibrating Air Column
A vibrating air column refers to the air inside a tube that vibrates when the tube is acted upon by a sound wave. The script discusses a tube open at both ends, which is an example of a system where an air column can vibrate and resonate at certain frequencies.
πŸ’‘Velocity of Sound (V)
The velocity of sound is the speed at which sound waves propagate through a medium, typically measured in meters per second (m/s). In the script, the velocity of sound is given as 340 m/s, which is the standard speed of sound in air at room temperature and is used to calculate the wavelength and other properties of the sound wave.
πŸ’‘Wavelength (Ξ»)
Wavelength is the physical length of one complete cycle of a wave, measured from one point of corresponding phase on one wave to the same point on the next wave. In the script, the wavelength is calculated in relation to the length of the tube and the frequency of the sound wave, which is essential for understanding the resonance conditions.
πŸ’‘Resonance
Resonance in physics occurs when an object naturally vibrates at its maximum amplitude at a specific frequency, known as the resonant frequency. The script discusses the conditions for resonance in an air column within a tube, which is a fundamental concept in acoustics.
πŸ’‘Length of the Tube (L)
The length of the tube is a critical parameter in determining the resonant frequencies of the air column inside. In the script, the length is calculated based on the given velocity of sound and the fundamental frequency, and it is used to analyze the behavior of the sound wave within the tube.
πŸ’‘Maximum Speed of Air Molecules
The maximum speed of air molecules refers to the highest velocity that the particles of air can attain during their oscillation within the tube. The script describes sketching a graph of this maximum speed as a function of position within the tube, which helps visualize the distribution of energy in the vibrating system.
πŸ’‘Graph
A graph is a visual representation of data, showing relationships between variables. In the script, the coach discusses sketching a graph to represent the maximum speed of air molecules as a function of position within the tube, which is a way to illustrate the sinusoidal pattern of particle velocity in a standing wave.
πŸ’‘Standing Wave
A standing wave is a wave that remains in one place, with nodes (points of no displacement) and antinodes (points of maximum displacement). The script mentions the formation of a standing wave within the tube when it is closed at one end, which changes the resonance conditions and the resulting wave pattern.
πŸ’‘Node
In the context of waves, a node is a point of minimum or no displacement that remains stationary while other parts of the wave oscillate. The script refers to the nodes being at the center and the ends of the tube when it is closed at one end, indicating the points where the air molecules have zero velocity.
Highlights

Introduction to the 2019 AP Physics 1 free response question 5 by Allen from Bothell STEM.

Explanation of a tuning fork vibrating at 512 Hertz and its relation to the open tube.

Fundamental frequency and its calculation using the velocity of the air column.

The formula for calculating the length of the tube L in terms of velocity and frequency.

Conversion of the velocity of air from m/s to a frequency value.

Calculation of the tube length L as 0.332 meters using the given formula.

Instructions to sketch a graph of the maximum speed of air molecules in the tube as a function of position X.

Discussion on the sinusoidal nature of the maximum particle speed graph.

Explanation of the maximum and minimum points of the sinusoidal speed graph.

Transition to a new scenario where the tube is kept shut at the right end.

Analysis of the change in the fundamental frequency with the tube being closed at one end.

Calculation of the new wavelength in the closed tube scenario, which is four times the length of the tube.

Derivation of the formula to calculate the new fundamental frequency F with the closed tube.

Final calculation of the new fundamental frequency as 750 Hertz.

Music interlude indicating a transition or conclusion in the discussion.

Transcripts

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Physics TutorialResonant FrequenciesSound WavesAP PhysicsWave BehaviorEducational ContentSTEM CoachFundamental FrequencyWave SpeedBothell STEMAcoustics