QUIZ 3 CH. 15, 16
discussion questions, exercises, problems--http://www.masteringphysics.com
     
CLICK HYPERPHYSICS  FOR SUMMARIES OF  ALL UNDERGRADUATE  PHYSICS TOPICS  INCLUDING RELATIVITY, ATOMS, NUCLEI AND COSMOLOGY.
CLICK HERE FOR WAVES IN VIDEO.
CHECK BACK LATER FOR HELPFUL DISCUSSIONS
Exercise 15.4: Ultrasound Imaging; Exercise 15.6; Exercise 15.12: Speed of Propagation vs. Particle Speed;  Exercise 15.16; Exercise 15.20; Exercise 15.24; Exercise 15.38; Exercise 16.33;  Exercise 16.35;  Problem 16.70 ;
The traveling and standing wave problems are straightforward and will be considered last; let's first explore interference: CH. 16; we assume a common detector receives waves from two sources and the path  difference between the two waves produces constructive or destructive interference. Remember constructive means  path difference  = n*lambda and destructive means path difference = (2*n + 1)*(lambda/2);  n = 0, 1, 2, 3,4, ..... Usually the path difference is found using 1D or 2D Euclidian geometry  as shown  below. Meanwhile, the sample exams' treatment of interference  here defines/extends the envelope.
33. In this case, the path difference is fixed at 2.00 m but we are changing the wavelength to achieve conditions of constructive or destructive interference.
(a) constructive:  2.00 = n*lambda, n =  0, 1, 2, 3, 4, ..But wave speed =  v = w/k =  lambda*f.  Let v = 344 m/s, the speed of sound in air at room temperature 20 degrees Celsius. Thus 2.00 m = n*v/f, or f = n*v/(2.00 m). What is the lowest non -zero value of f?
(b) destructive: 2.00 = (2n+ 1)*(lambda/2), n =  0, 1, 2, 3, 4,  with wave speed =  v =  lambda*f.   Thus 2.00 m =
(n+1/2)*v/f, or f = (n+1/2)*v/(2.00 m). What is the lowest non-zero value of f?
35. LET DA be the distance between  you and speaker A and  DB how far you are from speaker B.  Thus DA + DB =
12 m. DB - DA = n*v/f for constructive interference, n = 0, +  or -1  + or - 2, + or -3, ..... and   DB - DA = (n + 1/2)n*v/f for destructive interference,  n = 0, +  or -1  + or - 2, + or -3, ...
Suppose you are at a position of constructive interference; then DB - DA = n*v/f  for a given n. If you now decrease
DB - DA, you would be walking toward speaker B.
Let's look at this problem more analytically then check with our physical intuition:

First let's solve for DB :

For constructive interference DB + DA = 12 and DB - DA = n*v/f, which leads to DB = n*v/(2f)  + 6.
For destructive interference DB + DA = 12 and DB - DA = (n+ 1/2)*v/f, which leads to DB = (n + 1/2)*v/(2f)  + 6.

Suppose we have constructive interference; thus DB - DA = n*v/f = n*lambda and   DB = n*v/(2f)  + 6. As we walk toward B to cause destructive interference  we decrease DB from n*v/(2f)  + 6  to (n - 1/2)*v/(2f)  +  6.  We see the difference is  -v/(4f) = -lambda/4, so  you'd walk one-fourth a wavelength toward B. Note if DB deceases by lambda/4, DA increases by lambda/4 and the path difference DB - DA =  lambda/2 as you would expect for destructive  interference.

70.  DISCUSSIONS SOON.