How Things Work - Fall 2018

Refraction : Consider a wave hitting a new medium - one in which is travels more slowly. This would be like light going from air into water. The light has a certain frequency (which is unchangeable, since its set by whatever atomic process causes it to be emitted). The wavelength has a certain amount set by the equation, c = f l, where l is the wavelength (Greek symbol, lambda). When the wave enters the new medium it is slowed - the speed becomes lower, but the frequency is fixed. Therefore, the wavelength becomes smaller (in a more dense medium). Note also that the wave becomes "bent." Look at the image above: in order for the wave front to stay together, part of the wave front is slowed before the remaining part of it hits the surface. This necessarily results in a bend. MORE DETAIL: The general rule - if a wave is going from a lower density medium to one of higher density, the wave is refracted TOWARD the normal (perpendicular to surfac...

Reflection - light "bouncing" off a reflective surface. This obeys a simple law, the law of reflection! The incident (incoming) angle equals the reflected angle. Angles are generally measured with respect to a "normal" line (line perpendicular to the surface). https://ricktu288.github.io/ray-optics/simulator/ Note that this works for curved mirrors as well, though we must think of a the surface as a series of flat surfaces - in this way, we can see that the light can reflect in a different direction, depending on where it hits the surface of the curved mirror. So - light reflects from mirrors, according to the law of reflection.  However, if the mirrors is curved, light still obeys this rule - it just looks a bit different.  You have to visualize the curved mirror as a series of little flat mirrors. A convex mirror (top) acts reflects light rays "outward" - the light rays  seem  as though they are coming from inside the conv...

Recall that waves can be categorized into two major divisions: Mechanical waves, which require a medium. These include sound, water and waves on a (guitar, etc.) string Electromagnetic waves, which travel best where there is NO medium (vacuum), though they can typically travel through a medium as well. All electromagnetic waves can be represented on a chart, usually going from low frequency (radio waves) to high frequency (gamma rays). This translates to: long wavelength to short wavelength. All of these EM waves travel at the same speed in a vacuum: the speed of light (c). The standard wave velocity equation is still: But for light, where c is the speed of light (3 x 10^8 m/s ): c = f  l Still, f is frequency (in Hz) and  l  is wavelength (in m).  Note that, depending on your browser, the lambda (Greek symbol for wavelength) may show as an l. (We will see during the next class that the speed of light, while constant i...

Doppler! The Doppler Effect First, some animation: http://www.lon-capa.org/~mmp/applist/doppler/d.htm http://falstad.com/ripple/ So above, the blue dot is emitting sound and moving to the right.  Since it is moving AND emitting sound at the same time, the waves are getting closer on the right - resulting in a shorter wavelength (or higher frequency).  And it is the complete opposite on the left. http://falstad.com/ripple/ Play with this and choose the "Doppler Effect 1" example. And for some more visuals: https://highered.mheducation.com/olcweb/cgi/pluginpop.cgi?it=swf::800::600::/sites/dl/free/0072482621/78778/Doppler_Nav.swf::Doppler%20Shift%20Interactive The key in the Doppler effect is that motion makes the "detected" or "perceived" frequencies higher or lower.   It's worth noting that the effect also works in reverse. If you (the detector) move toward a sound-emitter, you'll detect a higher frequency. If you...

Wave questions for practice 1.   Draw a wave and identify the primary parts (wavelength, crest, trough, amplitude). 2.  Calculate the speed of a 500 Hz wave with a wavelength of 0.25 m.   Show the full calculation with the formula. 3. What is the frequency of a wave that travels at 24 m/s, if 3 full waves fit in a 12-m space?  (Hint:  find the wavelength first.) 4.   What is the difference between mechanical and electromagnetic waves?  Give examples. 5.   Consider the musical note G, 392 Hz.  Find the following: a)     The frequencies of the next two G's, one and two octaves above . b)     The frequency of the G one octave below than 392 Hz. c)     The frequency of G#, one semi-tone (piano key or guitar fret) above this G. d)     The frequency of A#, 3 semi-tones above G. e)     The wavelength of the 392 ...

Tonight we will chat about the most well-known of mechanical waves:  sound. Sound is a mechanical wave, meaning that it REQUIRES a medium through which to travel.  Whereas light (or other EM waves) can travel anywhere (more or less), and travel fastest (at the speed of light) through a vacuum, sound is restricted greatly.  It can only travel through a medium, which itself carries the vibrations that are sound waves. The same characteristics previously discussed still apply:  frequency, wavelength, speed, amplitude, crest, trough.  However, sound itself is a longitudinal wave (jiggling "back and forth") rather than a transverse wave (like EM waves, which vibrate "up and down"). Wave definitions to recall Frequency (f) - number of waves per second (measured in hertz, or Hz).  For sound, frequency refers to pitch.  Some frequencies are defined as notes Wavelength ( 𝝺 ) - the length of the wave, from crest to crest, etc. (in m). The...