1. (20 points)

A fireworks rocket explodes at a height r above the ground and sends out a spherical wave. See the diagram below. A detector D on the ground directly under the explosion measures an average sound level in decibels of 110 dB. (Please check out the reformulation that you did for extra credit...)

(a) ( 10 points) What is the intensity I of the sound that the detector measures ? Take the reference intensity to be I0 =1.00 x10-12 W/m2 .
(b) ( 10 points) The detector measures a total sound energy of 1.80x103 J. The sound signal lasts for 0.25 seconds. What is the height r above the ground ?

 

 

(a) 110 =10*log(I/I0).... Solve for I = 0.10 W/m2 
(b) I*time*Asphere =1.80x103 J......solve for the radius r = 75 m.

 

 

2. (30 points )

A tuning fork generates sound waves with a frequency 242 Hz. The waves travel in opposite directions along the hallway, are reflected by the walls and return to the tuning fork. The hallway is 45.0 m in total length, and the tuning fork is located 13.0 m from one end as shown below in the diagram

(a) (28 points) What is the phase difference in radians when the waves meet at the tuning fork again? The speed of sound in air is 343 m/s.
(b) (4 POINTS) Find the distance d from the end  such that there is a minimum in sound....

(a) path difference = 2(45 - 13 -13)= 38 m...thus phase difference = k*38 =168 rads....Note that you get k from the wavelength = 343/f = 343/242=1.417 m.... . Remember the definition of k??
(b) 2*(45 - 2d) =(2n + 1)*wavelength/2 
d = 22.5 - (2n+ 1)*wavelength/8...assuming n<0,  as | n | gets bigger, d gets BIGGER .....d can never be greater that 45 m... so find n such that this is just true.....we get:
45 > 22.5 - (2n+ 1)*wavelength/8 so that (2n+ 1)*wavelength/8 >-22.5 or
n .> -22.5*4/wavelength -1/2 = -90/1.417 - 0.5 = -64.014 or n > -64.014 so choose n = -64 to get the maximum d...we have:
d = 22.5 - (2*[-64.014] + 1)*1.417/8= 44.9 m

 

3. (30 points)

A dish antenna with a diameter of 20.0 m receives (at normal incidence) a radio signal from a distance source. (In fact, it is thought to be an extraterrestrial message from an advanced culture as in the movie "Contact".) The radio signal is a continuous sinusoidal wave with amplitude Em = 0.200 . Assume that the antenna reflects 80% of the incident radiation.

  1. (5 points) What is the amplitude Bm of the magnetic field in this incident wave?
  2. (12 points) What is the radiation pressure exerted on this antenna?
  3. (8 points) What is the force exerted on this antenna?
  4. (5 points) How much energy (in Joules) is absorbed by the antenna in 2 minutes = 120 seconds?

 

a. Em =Bm/c

b. P = 1.8S/c 
where, 

c. F = P*area

d. Energy = 0.2S*area*time

 

 

4. (9 points) EXTRA CREDIT.

A submarine is 310 m horizontally out from the shore and a depth D beneath the surface of the water. Please see the diagram below. A laser beam is sent from a tall building that is H = 105 m high so that it strikes the surface of the water at a point 220 m from the shore. The beam strikes the submarine. Note that nAIR = 1 and nWATER = 1.33.
(a) (4 points) Find D.

(b) (5 points) How many seconds does it take laser light to travel from the top of the building to the submarine?


(a) See sample exam #2, Problem 3. This problem is done in "reverse."
(b) time = d1/v1   + d2/v2   where d12 = 1052 + 2202   and d22= 902 + D2   from part (a) .......v1 = c  and v2 = c/1.33