1: Vibrations
- Page ID
- 134546
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- Describe vibrations using basic terminology: period, frequency, amplitude, fundamental frequency, spectral content
- Describe the relationship between period and frequency and apply it to problems
- Recognize that complicated vibrations are combinations of simpler vibrations all happening simultaneously
- Compare and contrast simple harmonic motion (SHM), complex vibrations, noise and transients
- Interpret time domain graphs of vibrations
- Interpret frequency domain graphs of vibrations
Vibrations cause sound. Strike a tuning fork with something soft (your knee, a rubber mallet) and you hear a tone. Touch the tines of the tuning fork to the hairs on your arm and you feel a soft tickling sensation. Touch a stereo speaker while it’s producing sound, and you feel the vibrations.
When something vibrates, it disturbs the material that surrounds it- usually air. When vibrations arrive at a detector (like your ear or a microphone), the detector turns those vibrations into electrical signals that can be interpreted or recorded. Devices like human ears and microphones that turn vibrations into electrical signals which can be recorded and/or interpreted are called transducers.
This part of the book focuses on vibrations in detail.
- 1.1: Anatomy of a vibration
- This page covers vibrations, defining periodic and aperiodic types while emphasizing frequency and period's roles in sound understanding. It illustrates these concepts with examples like hummingbird wingbeats. It also explores noise and amplitude, distinguishing random vibrations from measurable sound, with units such as Pascals and decibels for expressing sound levels.
- 1.2: Time graphs of common sounds
- This page covers sound vibrations and their time domain graph representation, introducing simple harmonic oscillation (SHO) characterized by sine curves. It explains that most musical sounds are complex vibrations made up of multiple SHO components, influencing pitch and timbre through fundamentals and overtones. Additionally, it addresses aperiodic sounds, or noise, which do not have a repeating pattern and cannot be described with conventional frequency concepts.
- 1.3: Amplitude and period on time graphs
- This page explains the extraction of period and amplitude from time domain graphs, detailing how to measure horizontal and vertical distances. It covers the fundamental period for complex vibrations and provides equations for calculating cycles and frequency based on graph points. An example demonstrates measuring period and amplitude, emphasizing the importance of unit labels on axes for accurate interpretation of time and amplitude values.
- 1.4: FFTs and spectrograms
- This page discusses frequency domain graphs, or FFT graphs, detailing how they showcase vibration frequencies over time, with pure tones as single peaks and complex vibrations as multiple peaks. It also covers spectrograms that integrate time and frequency, emphasizing the importance of resolution balance.
- 1.5: More about overtones
- This page explores the vibrations of musical instruments, emphasizing overtones and harmonics. It details how instruments create sounds with varying harmonic structures, noting that harmonics are multiples of the fundamental frequency. String and wind instruments typically produce harmonics, whereas chimes produce anharmonic overtones. The page highlights consistent spectral content across different notes on the same instrument and discusses the connection between harmonics and musical intervals.
- 1.6: Vibrations- Review and homework
- This page explores key concepts of vibrations and oscillations, defining terms such as amplitude, frequency, and period. It discusses the interplay between time domain and frequency domain graphs and includes questions to enhance comprehension. Practical numerical problems on fundamental frequencies and vibrations are featured, alongside hands-on activities using tools like tuning forks and Audacity. The overall focus is on understanding the characteristics and analysis of sound waves.
Thumbnail: Green and white line illustration. (Unsplash License; Denis Sebastian Tamas on Unsplash)