Comments on IQs for Wednesday, January 26:
1) (E,p263) In general, the sounds from the two speakers of a stereo
don't have the same wavelength and are not "coherent" = coordinated = definite
relations between their respective crests, etc. So there is no interference
in general. If there were some instants when conditions for interference
existed, and the leads were interchanged, constructive interference would
become destructive and vuce-versa.
(#6, p.263) Generally, time of travel is distance traveled divided by speed of travel Thus:
(a) Light-3km/300,000 km/s (3km/ 3*105 km/s) = 1*10-5 s = 0.00001 seconds, certainly not very noticeable.
(b) Sound-3km/0.340km/s = 3,000m/340 m/s =8.82 seconds, a very noticeable time. Thus you see the flash long before you hear it.
(#7, p.263)(a) The fundemental note on a string only has nodes at the ends of string, 1 meter apart in this case. Since the wavelength is twice the distance between nodes, the wavelength is 2 meters. (b) Since the wave velocity is the product of the frequency and the wavelength, the speed is 440Hz*2m = 880 m/s (since 1 Hz = 1 s-1).
2) If you will look at Fig 7-10, page 89 of the March text, you will see that the wave length of microwaves is greater than that of infra-red, the frequency of microwaves less than that of infr-red. Your stove gives off infra-red radiation, your microwave oven obviously uses microwaves. The fact that the latter, in some cases, cooks faster than the former has nothing to do with which frequency is greater but with which frequency is more in resonance with the molecular vibration frequencies of the food being cooked.
Communication with Students
4 February, 2000
A number of you had difficulty with today’s IQ. Here are some
Jane says Joe is 100miles*cosine(10o) = 98.4miles North, 100miles*sine(10o) = 17.4miles east of her.
Joe says Jane is 100 miles South, 0 miles east of him.
They both agree that they are a distance of 100 miles = Square root [(98.4)2 + (17.4)2] apart.
b) For this problem, gamma = 3.20.
Thus, while Jane thinks it takes 30 minutes for her breakfast, Joe thinks it takes 30*3.20 = 96.1 minutes.
While Jane thinks it takes 15 minutes to walk back, Joe thinks it takes 15*3.20 = 48 minutes.
While Jane thinks she has walked a distance of 0.5 km, Joe thinks she has walked 0.5/3.20= 0.16km.
They will agree on “proper times”(rest times) and “proper lengths” ( rest times). For example, J ane thinks she is at rest while eating: delta x = 0, delta t = 30 minutes = 1800seconds.
For Joe, delta t’ = 96.1 minutes = 5.77*103 seconds and during this time she has moved (with her space ship) a distance of delta x’ = 0.95c*96.1 minutes = 1.64*1012 meters (distamce = speed *time) . If you calculate Joe’s space -time interval, you get
(1.64*1012 meters)2 - (c*5.77*103 seconds)2 = - 3.0*1023 meters squared.
Jane’s space-time interval is just - (c*1800 seconds)2 = - 2.91023 which is the same number, given rounding errors. Thus the two space-time intervals are both the same, time-like, both proper times.
Try doing the same kind of calculation for her walk - its somewhat more complicated, but again you get an agreed upon space-time interval, this time, space-like.
7 February 2000
BRINGING TOGETHER SEEMINGLY OPPOSING CONCEPTS
SOMETIMES LEADS TO INTERESTING NEW UNDERSTANDINGS
Concept Very different
Terrestrial Physics Celestial Physics Galileo “New” Physics
Falling Apple Falling Moon Newton Universal Gravitation
Inter-particle forces -Action-at-a-distance Faraday Field lines
Electricity Motion Oersted Magnetism
Electricity Magnetism Maxwell Electromagnetic Fields
Galilean Relativity- Maxwell’s Equations Einstein Special Relativity
Space Time Einstein Space-Time
Lorentz Contraction -Time Dilation
Mass Energy Einstein Creation of matter and the universe
Cons. of Energy -Cons. of Momentum
Rest mass as invarient
Special Relativity -Gravitation Einstein General Relativity
General Relativity- Hubble Expansion Gamow et al “Big Bang”
Particles Waves Schrodinger,etc Quantum Mechanics
Quantum Mechanics -Special Relativity Dirac, et al Quantum Field Theory
Electromagnetism -Weak Interactions Gell Man et al Electroweak Theory
Strong Interactions -Electroweak Theory Gell Man et al “Standard Theory”
General Relativity-Quantum Mechanics