# Waves and Sound

Student Learning Objectives
Lessons / Lecture Notes
Important Equations
Example Problems
Applets and Animations
Videos

Student Learning Objectives

• To visualize wave motion and develop intuition about waves.
• To understand how waves travel through a medium.
• To understand the difference between transverse and longitudinal waves.
• To become familiar with the properties of sinusoidal waves, such as wavelength, wave speed, amplitdue, and frequency.
• To study the properties of common waves - waves on strings, sound waves, and light waves.
• To apply energy and power concepts to waves.
• To use the decibel scale for sound intensity.
• To understand the Doppler Effect.

Lessons / Lecture Notes

The Physics Classroom (conceptual)

PY105 Notes from Boston University (algebra-based):

HyperPhysics (calculus-based)

PHY2048 notes from Florida Atlantic University (calculus-based):

General Physics I notes from ETSU (calculus-based)

Important Equations

Example Problems

Problem 1
(a) The middle C string on a piano is under a tension of 944 N. The period and wavelength of a wave on this string are 3.82 ms and 1.26 m, respectively. Find the linear density of the string.

(b) A string of length 0.500 m is fixed at both ends. The string is plucked and a standing wave is set up that is vibrating at its fourth harmonic. The traveling waves that make up the standing waves have a speed of 140 m/s. What is the frequency of vibration? (Solutions)

Problem 2
Two submarines are underwater and approaching each other head-on. Sub A has a speed of 12.0 m/s and sub B has a speed of 8.00 m/s. Sub A sends out a 1550 Hz sonar wave that travels at a speed of 1522 m/s. (a) What is the frequency detected by sub B? (b) Part of the sonar wave is reflected from B and returns to A. What frequency does A detect for this reflected wave? (Solutions)

Applets and Animations
 Traveling Waves Illustrating the sign of the time term for traveling waves moving from left to right or right to left. Transverse Wave The Transverse Wave model displays the motion of a transverse wave on a string.  The simulation allows an arbitrarily polarized wave to be created. Transverse Traveling Wave This applets shows a transverse traveling wave. The user can control the amplitude, wavelength, and frequency of the wave. Longitudinal Wave This applets shows a longitudinal traveling wave. The user can control the amplitude, wavelength, and frequency of the wave. Wave Representations The Wave Representations model displays two representations of a sinusoidal wave on a string.  One shows a movie of the wave traveling along a string - you can think of this representation as a sequence of photographs. The second representation is a plot of the displacement as a function of time for two points on the string (you can select which two points to use). Wave Function Plotter The Wave Function Plotter model displays a one-dimensional wave function u(x,t) depicting a disturbance at position x and time t. The disturbance can be mass density, pressure, or electric field depending on the physical context. The default wave function is sinusoidal but any other analytic function can be entered in the text box. Sound This simulation lets you see sound waves. Adjust the frequency, volume, and harmonic content and you can see and hear how the wave changes. Move the listener around and hear what she hears. Pressure and Displacement Waves This animation shows air molecules vibrating, with each molecule "driving" its neighbor to the right. It is used to illustrate that when the displacement wave is at a maximum then the density of the molecules, and thus the pressure wave, is at a minimum and vice versa. Tuning Fork A small animation of a vibrating tuning fork producing a sound wave. Doppler Effect The Doppler Effect model displays the detection of sound waves from a moving source and the change in frequency of the detected wave via the Doppler effect. In addition to the wave fronts from the source a graph depicting the time of emission and time of detection of each of the wave fronts is given. Doppler Effect Example This applet shows an emergency ambulance with switched on siren as it passes a person who is standing still at the street. Doppler Effect Explanation Illustrating the classical Doppler Effect for sound waves. Doppler Wave Fronts Illustrating the wave fronts of a wave for a moving source. Doppler Effect This applets shows the waves generated by a moving source. Click anywhere within the gray area and drag the mouse. An arrow representing the source velocity vector will appear. Let go of the mouse, and your source will move across the screen, emitting waves. Physics of Music A very brief introduction to the physics and psychophysics of music, with an emphasis on temperament, the relationship between notes.

Videos

 Download video (0.3 Mb) Watch Streaming Interesting slow-motion video of a man getting shot in the chest by a BB. It is cool to see the resulting transverse wave. Download video (0.8 Mb) Watch Streaming Awesome video showing the resulting shock wave that occurs when a jet travels faster than the speed of sound. The region immediately behind the shock wave is cooler (because the air is less dense) which causes the water vapor in the air to condense. You can actually figure out how fast the plane is traveling by measuring the opening angle of the shock wave. Download video (0.8 Mb) Watch Streaming Another video showing a plane traveling faster than the speed of sound. This video has sound so you can hear the sonic boom.