# UTPA STEM/CBI Courses/Physics (Calculus Based)/Waves and Vibrations

Course Title: Calculus Based Physics I

Lecture Topic: Waves and Vibrations

Instructor: Dr. Liang Zeng

Institution: University of Texas-Pan American

## Backwards Design

[edit | edit source]**Course Objectives**

**Primary Objectives**- By the next class period students will be able to:- Know the definition of transverse waves, wavelength, frequency, period, and speed
- Know the mathematical equation for a wave propagating along the x-direction as a function of time and know the definition of wave number
- Know that the direction of the wave propagation along the x-direction is reflected in the mathematical equation for wave propagation (-vt and +vt)
- Know that the speed of sound varies in different media (air, water, glycerol, etc.)
- Know the mechanism of sound propagation in air, including compression and rarefaction (longitudinal waves)
- Know the Doppler effect and its applications
- Know how to determine observed frequency when the source of the sound is moving or the observer is moving (+ and – signs)
- Know the superposition principle of waves (destructive and constructive interferences)
- Know the definition and derivation of the wave function of standing waves
- Know the difference between transverse and longitudinal standing waves
- Know the definition of resonance and how resonance works
- Recognize that space distribution and time distribution are separate in the standing wave function, and how the standing wave function compares to the traveling wave
- Know the characteristics of standing waves (nodes, antinodes, harmonics/modes)
- Know how to recognize harmonics (1st, 2nd, 3rd, etc.)from diagrams
- Know the relationship between natural frequency, length, and speed in longitudinal standing waves of sound propagation in a tube

**Sub Objectives**- The objectives will require that students be able to:- text
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**Difficulties**- Students may have difficulty:- Understanding the signs that differentiate the directions of travelling waves
- Understanding the signs used in the Doppler effect formula
- Understanding how the standing wave equation (x and t are in separate terms) is different from the travelling wave equation
- Recognize harmonic drawings

**Real-World Contexts**- There are many ways that students can use this material in the real-world, such as:- Travelling waves: ripples in water, earthquake transverse S waves, earthquake longitudinal P waves, light waves*
- Transverse standing waves: string instruments, slinky, resonance cavity in lasers*
- Longitudinal standing waves: wind instruments, drums, convection currents on the sun*
- Doppler effect: ambulance siren, police car, echocardiogram, ultrasound, Doppler radar for wind speed and direction (page 439 Walker’s book)*
- Resonance: Tacoma Narrows bridge collapse, standing waves*

**Model of Knowledge**

**Concept Map**- text
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**Content Priorities****Enduring Understanding**- Definition of transverse waves, wavelength, frequency, period, and speed
- Mathematical equation for a wave propagating along the x-direction as a function of time and the definition of wave number
- The direction of the wave propagation along the x-direction as reflected in the mathematical equation for wave propagation (-vt and +vt)
- The mechanism of sound propagation in air, including compression and rarefaction (longitudinal waves)
- Determine observed frequency when the source of the sound is moving or the observer is moving (+ and – signs)
- The superposition principle of waves (destructive and constructive interferences)
- The definition of the wave function of standing waves
- The difference between transverse and longitudinal standing waves
- The definition of resonance and how resonance works
- The characteristics of standing waves (nodes, antinodes)
- The relationship between natural frequency, length, and speed***text

**Important to Do and Know**- Know that the speed of sound varies in different media (air, water, glycerol, etc.)
- The Doppler effect and its applications
- The derivation of the wave function of standing waves
- Space distribution and time distribution are separate in the standing wave function, and how the standing wave function compares to the traveling wave
- Recognize harmonics (1st, 2nd, 3rd, etc.) from standing wave diagrams
- The relationship between frequency, length, and speed for 2nd and 3rd harmonics

**Worth Being Familiar with**- The equation for a simple harmonic oscillator in the vertical direction
- The formula for wave propagation speed as a function of tension in a string
- Sound intensity in decibels
- Frequencies for sonar applications (dolphins, bats, boats)
- Pressure variation along a tube in sound propagation (page 332 figure 12.11-12 Giancoli, “Physics” 6th edition)

**Assessment of Learning**

**Formative Assessment**- In Class (groups)
- In class exercises, flexible to the instructor, for formative assessment

- Homework (individual)
- Pay attention to the following new units:
- Self-reading Chapter 16: 16.1-16.2, 16.4; Chapter 17: 17.1-17.2, 17.4 (up to shock waves); Chapter 18: 18.1-18.5 in the textbook

- In Class (groups)
**Summative Assessment**- text
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## Legacy Cycle

[edit | edit source]**OBJECTIVE**

By the next class period, students will be able to:

- text
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The objectives will require that students be able to:

- text
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**THE CHALLENGE**

Instructions: Students can refer to any resource to answer this question. Each person needs to email the report to Mr. Manuel Lara, Teaching Assistant on WebCT which answers the question with supporting data linking back with the relevant physics content. The report is usually due a week from the date when the question is assigned and will be kept in a WebCT folder.

Rubric for grades (on a 0-10 point scale):

- List of resources (1 point)
- Correctly describing the periodic motions (3 points)
- Correctly describing the factor(s) contributing to the periodic motions and why the periodic motions caused the bridge to collapse (3 points)
- Making recommendations about how to avoid similar catastrophes (3 points).

Format:

- Put down your name
- State challenge question and its number
- Everything has to be typed, font is 12 point time-new roman style
- The text has to be at least 300 words minimum
- You can incorporate graphs, figures, tables etc.
- Save the report as .rtf file.

After viewing the Tacoma Narrows Bridge collapse video (Youtube source, keywords “Tacoma Narrows bridge”), describe the periodic motions of the bridge before it collapses, the factors contributing to the periodic motions, why the periodic motions caused the bridge to collapse, and make recommendations about how to avoid similar catastrophes in future suspension bridges.

**GENERATE IDEAS**

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**MULTIPLE PERSPECTIVES**

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**RESEARCH & REVISE**

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**TEST YOUR METTLE**

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**GO PUBLIC**

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## Pre-Lesson Quiz

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## Test Your Mettle Quiz

[edit | edit source]- (Wave propagation as a function of time, positive velocity: Serway 7th edition page 469 #17). A transverse wave on a string is described by the wave function: y=(0.120 m) sin(π/8 x+4πt)
- Determine the transverse speed and acceleration of the string at t = 0.200 s for the point on the string located at x = 1.60 m
- What are the wavelength, period, and speed of propagation of this wave?

- (Wave propagation as a function of time, negative velocity: Serway 7th edition page 469 #13). A sinusoidal wave is described by the wave function: y=(0.25 m)sin(0.30x-40t)where x and y are in meters and t is in seconds.
- Determine the amplitude for this wave
- Determine the angular frequency for this wave
- Determine the angular wave number for this wave
- Determine the wavelength for this wave
- Determine the wave speed for this wave
- Determine the direction of motion for this wave

- (Doppler effect, source of sound is moving, observer is stationary: Serway 7th edition page 496 #35). Standing at a crosswalk, you hear a frequency of 560 Hz from the siren of an approaching ambulance. After the ambulance passes, the observed frequency of the siren is 480 Hz. Determine the ambulance’s speed from these observations.
- (Doppler effect, source of sound and observer are moving: Serway 7th edition page 496 #33 a and b). A driver travels northbound on a highway at a speed of 25.0 m/s. A police car, traveling southbound at a speed of 40.0 m/s, approaches with its siren producing sound at a frequency of 2 500 Hz.
- What frequency does the driver observe as the police car approaches?
- What frequency does the driver detect after the police car passes him?

- (Standing waves: Serway 7th edition page 527 #29). Calculate the length of a pipe that has a fundamental frequency of 240 Hz assuming the pipe is
- closed at one end
- open at both ends

- (Resonance: Serway 7th edition page 526 #28). The figure below (part a) (insert figure) is a photograph of a vibrating wine glass. A special technique makes black and white stripes appear where the glass is moving, with closer spacing where the amplitude is larger. Six nodes and six antinodes alternate around the rim of the glass in the vibration photographed, but consider instead the case of a standing-wave vibration with four nodes and four antinodes equally spaced around the 20.0-cm circumference of the rim of a goblet. If transverse waves move around the glass at 900 m/s, an opera singer would have to produce a high harmonic with what frequency to shatter the glass with a resonant vibration as shown in the figure (part b)?
- (Natural frequency, length, and speed: Serway 7th edition page 527 #36). A tunnel under a river is 2.00 km long.
- At what frequencies can the air in the tunnel resonate?
- Explain whether it would be good to make a rule against blowing your car horn when you are in the tunnel.