Name:
PHYSICS 232
Final Examination, May 3, 1996, 9:00am-12:00pm
Instructor: P. Q. Hung
10 points for each problem. READ the problems carefully. SHOW YOUR WORK. DO NOT JUST write the answers down.
Useful formulas (not necessarily applied to all problems below):
, 
, 
,
, 
, 
, R = V/I
, 
,
,
,
,
,
, 
, 
, 
, 
.
, 
phase change
,
sin(a) + sin(b) = 2 sin[(a+b)/2] cos[(a-b)/2],
,
,
, 
kg
, 
, 
m/s
1 N/C = 1 V/m, 1 V = 1 J/C, 1 A = 1 C/s, 1 T. 
= 1 V.s
1) A spider of mass 0.36 g sits in the middle of its horizontal web, which sags 3.00 mm under its weight. Estimate the frequency of vertical vibration for this system assuming that it behaves like a spring.
In order for the spider to be in equilibrium, we must have
) Consider traveling waves moving in opposite directions, one of
the form 
, and the other
of the form 
. (a) Find the resultant
wave and describe its nature. (b) What are the locations of the nodes
of this resultant wave?
This is a standing wave vibrating with a frequency of 
and having nodes when 
, i.e. when 
) Two identical piano wires have a frequency of 512 Hz when under
the same tension. As a consequence of slippage, the tension of one
of the wires changes slightly, so that its frequency decreases slightly.
If 4 beats/s are heard ( 
= 4 beats/s) when the wires
both vibrate, what is the fractional change in the tension, dT/T, of
the lower-frequency string?
For the fundamental frequency, 
So 
, which means 
