Physics of Sound & Music: Day 3 Wave Properties & Behaviors I

Scientific Notation and Prefixes Scientific notation allows us to handle very large or very small numbers in a clear manner becomes 6.02x becomes 16x m Prefixes are shorthand for scientific notation. The most common are shown to the right I'm going to assume you are ok with this. If not, stop by for some help! 2

Wave Parameters 3 –Wavelength: If you “freeze” the wave for a moment, wavelength is the distance from any point on the wave to the next similar point. Peak to peak or trough to trough is usually the easiest way to see wavelength. –Amplitude: How “big” the wiggles in the medium are. Measured from center to extreme, which gives half of the total motion width. Note: For all waves, the energy carried depends on the amplitude squared. –Frequency: How many times a part of the medium gets wiggled each second. Measured in cycles per second, or hertz (Hz). The wave and its source share the same frequency. –Wave speed: How quickly the wave (disturbance) moves through the medium. Measured just like any other speed, meters per second or miles per hour, etc. There are a few important quantities we need to use when describing waves: Wave Speed Wavelength Amplitude Frequency

SHM & Wave Summary Simple Harmonic Motion: –Requires a linear restoring force Properties: Period (T)Frequency (f) Amplitude (A)Phase Waves: –A traveling disturbance in some medium –Two types: Transverse & Longitudinal Properties:Wavelength (λ)Wavespeed (v) The speed of sound in air is 343 m/s (at 20° C) 4

In the animation, the two waves have A)The same wavelength but different frequencies. B)The same amplitude but different wave speeds. C)Different frequencies and different amplitudes. D)The same amplitude but different frequencies. E)Different wave speeds and different frequencies. 5

6 Human ears can generally detect sounds that have frequencies between 20 Hz to about 20 kHz. What is the largest wavelength we are able to hear? A)About 17 millimeters B)About 1.0 meter C)About 20 centimeters D)About 17 meters E)About 20 kilometers

Huygens's Principle Understanding how waves bounce and bend is easier if we first think of their basic movement in a more complicated way. Huygens's principle says that you can treat every point on a wave front as if it were a tiny wave source itself. The combination of all these tiny wave sources gives rise to the next wave front. 7

Superposition The property of superposition is one of the ways that we distinguish a wave from a physically solid object. Remember that waves don't transmit matter… only the disturbance travels. Superposition tells us that when two waves interact, they do not affect each other in any way. The total effect of the two waves can be found by simply adding them together… A+B. 8 + =

1/r 2 and Polarization Sounds get weaker with distance because the energy in the original sound spreads out over larger and larger areas. Because the area of a sphere is calculated as 4πr 2 this means… Polarization is a property only of transverse waves, so it will only be important when we discuss waves in solid materials (such as a violin string). The most common application of polarization is in sunglasses… 9

WarmUp Response: Mirror Image Consider the figure to the right: An observer O, facing a mirror, observes a light source S. Where does O perceive the mirror image of S to be located? ~0% →1 ~5% →2 ~20% →3 ~75% →4 10

WarmUp Response: Mirror Image “the mirror image of S would be perceived at spot #4. At first thought, I chose spot #3. I figured that the image would be like a light ray and bounce off the mirror at the angle at which it hit the mirror, but just to make sure, I did a little experiment at home with a box and a mirror. It seemed to me that I was looking through the mirror at the box, past spot #3 and into #4. I realized then that the mirror not only reflects the box, but also the space between the box and the mirror, so instead of seeing the box right up against the mirror (as if it were a window), it would appear as far away from the far side of the mirror as it was placed on my side.” 11

Reflection via Huygens No surprise that sound waves reflect off of surfaces. Even the mechanics of the reflection is unsurprising to most. Note: In physics we measure the angle relative to the normal. But this does give us a chance to see Huygens's principle at work… More complex shapes can reflect sound in useful ways, such as a parabolic reflector. 12

Reflection Examples Waves don't just reflect off of "solid" surfaces, any abrupt change in medium will cause some sound to be reflected. Even going from inside a tube to outside a tube is enough of a change to cause reflection, something that is crucial to the functioning of wind instruments. 13

Reading: Thursday (8/28) → 2.4 – 2.6 Notes: Homework #1 due today by 5 PM! WarmUp due Wednesday night by 10 PM Homework #2, due Tuesday by 5 PM: Ch. 2: Q: 1, 2, 4, 12* P: 2, 6, 7 +Theory Course Schedule is always found on the Course Home Page. 14