# 2019 AP Physics 1 Solutions Free Response #5

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

- 馃摎 The video is a lecture by Allen from Bothell STEM, focusing on the 2019 AP Physics 1 free response question 5.
- 馃幍 The subject matter involves a tuning fork vibrating at 512 Hertz and a tube that resonates at its fundamental frequency.
- 馃搹 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.
- 馃敘 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.
- 馃搲 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.
- 馃寪 The amplitude of air molecule velocity is related to the energy, which is proportional to the square of the velocity.
- 馃攧 When one end of the tube is closed, the fundamental frequency changes, and the wavelength (位) becomes four times the length of the tube.
- 馃敘 The new fundamental frequency is calculated using the formula F = V / (4L), resulting in 750 Hz for the closed tube scenario.
- 馃搳 The video emphasizes the importance of understanding wave properties, such as nodes and antinodes, in the context of resonating air columns.
- 馃幖 The lecture aims to help students visualize and calculate wave behavior in different configurations of air columns within a tube.
- 馃摎 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

##### 馃敩 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 (位) is twice the length of the tube when open at both ends. He then uses the formula 位 = 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

##### 馃挕AP Physics 1

##### 馃挕Free Response Questions

##### 馃挕Fundamental Frequency

##### 馃挕Vibrating Air Column

##### 馃挕Velocity of Sound (V)

##### 馃挕Wavelength (位)

##### 馃挕Resonance

##### 馃挕Length of the Tube (L)

##### 馃挕Maximum Speed of Air Molecules

##### 馃挕Graph

##### 馃挕Standing Wave

##### 馃挕Node

###### 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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