1.  A string fixed at both ends is vibrating in a standing wave at its fundamental resonance frequency. The string vibrates according to the equation
 y(x,t) =  0.02 sin(¶x/2)cos(20¶t)
 where x and y are in meters and t is in seconds.
(a)  Write the equations for two traveling waves that when superimposed produce the standing wave given above.
(b)  What is the frequency of the wave?
(c) What is the length of the string?
 (d) What is the velocity of a segment of the string, as a  function of time, at x = 1 m. Is this position of the string a node, an antinode or neither?
(e) If the mass of the string is 50 g, what is the tension in the string?
 

2.   A student stands between two organ pipes. Pipe A, open at both ends, has a length of 1.00 m and pipe B, closed at one end has a length of 0.51 m. The air column in each pipe is vibrating at its fundamental frequency. The speed of sound is 330 m/s.
(a)  What beat frequency does the student hear between the two organ pipes?
(b)  The student now runs at a constant speed of 4 m/s towards pipe A and away from pipe B. What beat frequency does the student now hear between the two pipes?
(c)  If the student detects an  intensity of 10^-4 W/m² for the sound from pipe A and pipe A has a sound level of 20 dB greater than pipe B, what is the sound intensity of pipe B?
 

3.  An aquarium filled with water (n_water = 1.33) has flat glass sides whose index of refraction is 1.52. A beam of light from outside the aquarium strikes the glass at an angle of 43.5^o relative to the normal from the glass surface.
a) What is the angle of the light ray in the glass, relative to the normal?
b) What is the angle of the light ray in the water, relative to the normal?
c) What would be the angle of the light ray in the water, relative to the normal, if it entered the water directly without passing through the glass?
d) What is the critical angle for a light ray in the glass, at the glass water interface?
 

4.    An object 5 cm high is placed 32 cm to the left of a thin converging lens of focal length f = 24 cm.
 (a)  Where is the image of the object located? Is the image real or virtual? Is the image erect or inverted? What is the size of the image?
 (b)  Now a thin diverging lens of focal length f = - 60 cm is placed 66 cm to the right of the converging lens. Where is the final image of the object now located relative to the converging lens? Is the final image real or virtual? Is the final image erect or inverted? What is the size of the final image?