3: Traveling waves
- Page ID
- 134564
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\( \newcommand{\dsum}{\displaystyle\sum\limits} \)
\( \newcommand{\dint}{\displaystyle\int\limits} \)
\( \newcommand{\dlim}{\displaystyle\lim\limits} \)
\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)
( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\id}{\mathrm{id}}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\kernel}{\mathrm{null}\,}\)
\( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\)
\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\)
\( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)
\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)
\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)
\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vectorC}[1]{\textbf{#1}} \)
\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)
\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)
\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- Distinguish between the motion of a wave and motion of the material in which the wave travels
- Distinguish between pulse and wave
- Describe the motion of a sound wave
- Describe the motion of the air particles in a sound wave
- Distinguish between longitudinal and transverse waves
- Define and describe wavelength, frequency and amplitude for L-waves and T-waves
- Explain the relationship among wave speed, frequency and wavelength
- Identify things that affect the speed of a wave (and things that don’t)
- Apply the equations \(d=vt\) and \(\lambda = \dfrac{v }{f}\) to solve numerical and non-numerical problems
- Describe Doppler effect and apply the Doppler effect equation:
Sources of sound vibrate. A short time later, the disturbance arrives at a detector and the detector vibrates in response to the disturbance. But what happens in between source and detector? What does sound look like as it travels?
Sound has a lot in common with ripples on a pond. Dip your finger in a pond and ripples travel outward from the the source. Dip your finger repeatedly, and a series of ripples travels outward from the source. Sound “ripples” are almost impossible to see directly, but there’s plenty of reason to believe they exist. A wave model for sound raises lots of questions about sound?
- What role does air play in sound?
- What, exactly, is moving when sound travels from place to place?
- How are the sound “ripples” made? What do they look like?
- How are loud sounds different from those quiet sounds?
- How are high pitch sounds different than low pitched ones?
- 3.1: How sound moves
- This page explores the speed of sound, approximately 340 m/s in air, varying with temperature and medium properties. Sound needs a medium, traveling fastest in solids. Its speed remains constant regardless of frequency or amplitude. Examples highlight sound delays, like perceiving lightning before thunder, and it includes a practical rule for estimating lightning distance based on the time delay between sight and sound.
- 3.2: Wave basics
- This page discusses the wave analogy for understanding sound, highlighting mechanical waves and the differences between transverse and longitudinal waves. Sound is defined as a longitudinal wave, where local molecular vibrations occur without the molecules traveling with the wave. Examples, such as a slinky and waves in a football stadium, illustrate these concepts. The page clarifies that sound travels as a disturbance, countering misconceptions about the movement of air molecules.
- 3.3: Wave anatomy
- This page explains the differences between pulses and waves, highlighting that waves require continuous vibrations. It covers key concepts like wavelength and amplitude—measuring wave distance and size/energy, respectively. In longitudinal waves, amplitude deals with density variations, while in transverse waves, it relates to vertical displacement. It also describes graphing techniques for longitudinal waves, focusing on pressure variations, and mentions online resources for wave visualization.
- 3.4: Microscopic model
- This page explores the dynamic characteristics of "still" air, emphasizing the rapid movement and frequent collisions of air particles traveling at roughly 1000 miles per hour. Despite this speed, they cover short distances between impacts, resulting in billions of interactions each second. Sound wave propagation in air is explained through the creation of compression and rarefaction regions, with minimal air particle movement.
- 3.5: Wavelength, speed and frequency
- This page discusses the relationship between wavelength, frequency, and the speed of sound, highlighting that wavelength is defined by the distance between wave pulses and is affected by frequency and medium speed. Lower frequencies yield longer wavelengths, while higher frequencies yield shorter ones. Sound speed increases in warmer air, impacting wavelength while leaving frequency unchanged. It includes interactive online simulations from PhET to explore these concepts further.
- 3.6: Doppler effect
- This page explains the Doppler effect, where the frequency of a wave differs due to movement between the source and observer. It provides examples such as race cars, illustrating how frequency changes when the source approaches or moves away. The mathematics behind the effect is introduced, with relevant equations for calculating observed frequencies.
- 3.7: Traveling Waves- Review and Homework
- This page covers key concepts and terminology related to waves, distinguishing between transverse and longitudinal types, along with properties like wavelength and amplitude. It explains sound propagation, factors affecting sound speed, and the interaction of waves with different materials. The page includes review questions to enhance comprehension and numerical problems that connect wave theory to real-world scenarios involving sound characteristics in various environments.
Thumbnail: Water drop in water in grayscale photograph (Unsplash License; Omar Gattis on Unsplash)