Useful number(s): Speed of sound in air: 343 m/s.
1) Speakers A and B emit a 775Hz sound wave in phase.
a) (3 pts.) Using speaker A you setup an experiment to measure the wavelength of the sound wave as it travels through 3 different materials. You measure a wavelength of 1.92m in material 1, 7.74m in material 2, and 0.44m in material 3. What is the sound speed in each material?
b) (3 pts.) Which material in part a) is most likely a liquid? A solid? A gas?
c) (10 pts.) After the experiment you place speakers A and B 0.94m apart in air. On the line joining the two speakers where will you find destructive interference?
d) (8 pts.) While you are listening to the silence of the destructive interference, someone grabs Speaker A, places it on a truck (still emitting a 775Hz sound), and speeds away from you at 32m/s. You run after the truck at 5m/s. Calculate the frequency you will hear? Does the pitch from the speaker sound higher or lower?
2) The A string on a guitar should have a fundamental frequency of 440 Hz.
a) (10 pts.) The string is 0.95m long and under a tension 514N when the string of the guitar is in tune (i.e., the fundamental frequency equals 440Hz). What is the mass of the string?
b) (5 pts.) What will be the frequency of the 2nd overtone (or 3rd harmonic)?
c) (5 pts.) A 440 Hz tuning fork was struck at the same time as the string was plucked and a beat was heard every 2 sec. Then a 445Hz tuning fork was struck at the same time as the string was plucked and a 4.5Hz beat frequency was heard. What is the frequency of the string?
d) (5 pts) You stand 1m from the guitar and measure the sound level of the guitar to be 32dB. What is the sound level where your friend is standing 2m away from the guitar? Assume that the sound from the guitar is spherically symmetric.
Useful number(s): k=8.99 x 109Nm2/C2
3) 2 charges are placed at the corners of a rectangle 3m tall and 4m wide: -1mC at bottom left and a 2mC at the top left.
a) (4 pts.) What is the electric potential at the top right corner?
b) (4 pts.) What is the electric potential at the bottom right corner?
c) (4 pts.) What is the work required to bring a -4mC from infinity to the bottom right corner?
d) (4 pts.) What is the work required to move the -4mC from the bottom right corner to the top right corner?
e) (6 pts.) What is the electric field vector at the top right corner?
f) (3 pts.) What is the force vector on the -4mC at the top right corner?
4) A 0.038g, -3mC charged insulated sphere is released from rest at the inner surface of a parallel plate capacitor with a constant electric field magnitude of 8500 N/C (See diagram). Ignore gravity in this problem.
a) (5 pts.) The sphere begins to move toward the other plate. Indicate the direction of the Electric Field on the diagram.
b) (5 pts.) How fast will the sphere be traveling when it hits the other side?
c) (5 pts.) What is the surface charge on the capacitor? Indicate the sign of the surface charge on the diagram.
d) (5 pts.) What is the potential difference across the capacitor?
e) (5 pts.) The total energy stored in the capacitor is 0.23J. What is the capacitance of the capacitor? What is the surface area of the parallel plates?