MUSICAL ACOUSTICS WAVES Science of Sound, Chapter 3

WAVE PROPERTIES: Reflection Refraction Interference Diffraction Doppler Shift WHAT IS A WAVE? Waves are disturbances that transport energy and information through a medium (but the medium itself is not transported). Waves can be longitudinal (e.g. sound waves) or transverse (e.g. waves on a string or water waves). ttp:// au/ // u/

REFLECTION OF AN IMPULSIVE WAVE At a fixed end At a free end

Traveling wave on a rope Reflection of a pulse: at a fixed end at a free end Mirror image of an impulsive wave approaching: A plane mirror (left) A corner mirror (right)

SUPERPOSITION OF WAVE PULSES (In continuous waves superposition can lead to either constructive or destructive interference).

INTEFERENCE OF TWO IDENTICAL WAVES ON A STRING At times t 1 and t 5 there is constructive interference; at time t 3 there is destructive interference. Note that at points marked N, the displacement is always zero; this represents a STANDING WAVE

REFLECTION OF PRESSURE (SOUND) PULSE CLOSED

SPEED OF SOUND IN IDEAL GAS

OCEAN WAVES WHEN THE WAVE ENTERS SHALLOW WATER IT SLOWS DOWN AND ITS HEIGHT INCREASES

DOPPLER EFFECT

Christian Doppler proposed the phenomenon in 1842 for light waves. In 1845 Dutch scientist Christoph Buys-Ballot developed a test for the Doppler shift of sound. A trumpet player sounded a note at 420 Hz while riding on a flatcar pulled by a locomotive. At the same time a stationary trumpeter played the same note. Buys-Ballot heard 3.5 beats per second. How fast was the train moving?

REFLECTION – WATER WAVES

REFLECTION – SOUND WAVES

REFLECTION

Signaling Mirror: A life-saving application of reflection How would you use a signaling mirror if you were in a lifeboat trying to attract attention from a passing airplane? See training film at: RrCVBaP0 (To construct your own signaling mirror see: o5Ci4-k)

REFRACTION TWO MEDIUMS (Index of refraction is a measure of how much waves are slowed down)

REFRACTION

REFRACTION THROUGH A PRISM ANGLE OF INCIDENCE

Rainbow over Hoover tower

IMAGES FORMATION BY LENSES REFRACTION OF LIGHT BY WATER

REFRACTION

DIFFRACTION When waves encounter an obstacle, they tend to bend around that obstacle. This is an example of diffraction. Diffraction is also apparent when waves pass through a narrow opening and spread out beyond it.

DIFFRACTION OF LIGHT AND SOUND WAVES

DIFFRACTION OF WATER WAVES BY A SLIT

It is the size of the opening (or barrier) compared to the wavelength that determines the amount of diffraction.

DIFFRACTION

Make a sketch (to scale) of: 1.Sound waves of 100 Hz radiated by a 10-inch speaker 2. Sound waves of 2000 Hz radiated by a 3-inch speaker 3. Sound waves of 5000 Hz radiated by a 3-inch speaker.

Refraction, Diffraction, and Interference of Water Waves

Wave Interference Interference between incident and reflected waves on a string leads to standing waves. Three-dimensional standing waves occur in a room due to interference between the incident wave and reflections from the walls, ceiling, floor, etc. Waves from two identical sources lead to maximum and minimum wave amplitudes in certain directions due to constructive and destructive interference.

INTERFERENCE OF WATER WAVES

INTERFERENCE OF WAVES FROM TWO IDENTICAL SOURCES

DIFFRACTION OF LIGHT BY A PIN

DIFFRACTION OF LIGHT BY A SCREW

DIFFRACTION OF LIGHT BY A RAZOR BLADE

DIFFRACTION BY A SINGLE SLIT

DIFFRACTION

Diffraction Grating A diffraction grating has many slits whose diffraction patterns combine to give bright and dark fringes (they could also be called “interference gratings”). A different pattern is created for each color (wavelength) of light, leading to some interesting patterns.

White light Compact fluorescent bulb LED bulb

Note the important difference between the spectra produced by a prism and by a grating: In spectra produced by a prism, violet light (shorter wavelength) is refracted through a greater angle than red light (longer wavelength). In spectra produced by a grating, however, red light is diffracted through a greater angle than violet light.

White light seen through a 2-D grating (from UNSW online demonstrations)

DIFFRACTION OF WATER WAVES

Assignment for Wednesday: Read Chapter 4 Homework: Exercises 1,3,4,5,7,8,10 (p.58) Extra credit: Write a short essay showing how the signaling mirror works (with diagrams). More extra credit: Construct a signaling mirror and demonstrate it to the class.

More extra credit: Read the article “Outdoor Sound Propagation in the U.S. Civil War (ECHOES 9, Winter 1999) and write a brief report. s/echoes/v9n1.pdf

LED SPECTRAL RESPONSE CURVE

SPECTRAL ENERGY DISTRIBUTION OF A WHITE LED