This is the 4th set of homework problems. These all come from Bloomfield's Student Supplement .

9.8. If astronauts landing on Mars were to find liquid water on the surface, the waves that they would see would behave somewhat differently. That's because the acceleration due to gravity on Mars is only 3.71 m/s2.

a. A wave always needs two forms for its energy. In a surface wave on water, one of those forms is gravitational potential energy. How would the gravitational potential energy of a wave on Mars compare with that of an identical looking wave on Earth?

b. The 'stiffness' of the water's surface depends on gravity. When gravity is weak, it takes less work to deform the water's surface. Use your answer to part a to show that this is the case.

c. The surface of water on Mars is more easily deformed and thus less 'stiff' than the surface of water on Earth. On which planet would surface waves on water travel faster, Mars or Earth?

d. Which wave carries more energy, a surface wave on Mars or an identical looking wave on Earth?

10.4. A nerve cell is an electrostatic device that operates very differently from a wire. It's a fluid-filled tube that's surrounded by another fluid. Both fluids contain ions (electrically charged atoms) of sodium, potassium, and chlorine. Each sodium or potassium ion has one elementary unit of positive charge while each chlorine ion has one elementary unit of negative charge. The wall of the nerve cell separates the two fluids and normally prevents these ions from passing through it.

a. When the nerve cell is in its resting state, the fluid outside it has slightly more sodium plus potassium ions than chlorine ions. The fluid inside it has slightly more chlorine ions than sodium plus potassium ions. What is the net electric charge of each of these two fluids?

c. To produce the electrostatic potential energy that results from separating the charges, the nerve cell pumps sodium ions out of the cell. Show that the nerve cell must do work on the sodium ions during this transfer.

d. Which part of the nerve cell has a positive voltage? Which part has a negative voltage?

e. When the nerve cell 'fires,' it abruptly allows sodium ions to pass through its walls. Which way do they move and what happens to the voltages of the various parts of the cell?

11.5. A typical audio speaker, such as that in a radio, consists of a permanent magnet, a coil of wire, and a movable speaker cone. The coil of wire is connected electrically to the radio's amplifier so that the radio controls how much current flows through the coil. The coil is attached to the speaker cone so that if the coil moves, the speaker cone moves and creates sound waves in the air.

a. When the amplifier sends an electric current through the coil, the coil accelerates backward or forward in the permanent magnet's magnetic field. Its copper wire isn't normally magnetic, so why does the coil experience forces from a magnet?

c. Pushing the speaker cone forward quickly compresses the air in front of the cone and requires energy from the radio. Show that the speaker cone does work on the air while compressing it.

d. When you talk in front of a speaker, the sound of your voice moves the speaker cone and the coil. The coil moves back and forth through the permanent magnet's magnetic field. What happens to the mobile electric charges in the wire coil?

12.3. The power supply in your stereo amplifier uses alternating current from the electric company to provide direct current to the amplifier. This supply converts electric power from one form to another through the use of transformers, diodes, capacitors, and transistors.

a. The power supply provides a relatively small voltage rise to the large current that it sends through the amplifier. The voltages provided by the electric company are too high for the amplifier and the currents are too small. How does a transformer make it possible for the power supply to provide a relatively small voltage rise to a relatively large current that flows between it and the amplifier?

b. The power supply's transformer provides AC electric power through two wires, but the amplifier needs DC electric power through two wires. To fix this mismatch, the stereo connects these two pairs of wires with four diodes so that even though the currents through the two wires of the transformer reverse, the currents through the two wires of the amplifier don't reverse. How are those four diodes connected between the transformer and amplifier? (Draw a picture and indicate which way current can flow through each diode.)

c. While the diodes (see part b) ensure that current always flows in one direction through the amplifier, the transformer can't provide current when the current from the power company is reversing. To maintain a steady current through the amplifier, the power supply uses a large capacitor. When the transformer's current is large, some of that current is used to transfer charge between the capacitor's plates so that it stores separated charge. When the transformer's current is small, this separated charge is allowed to flow through the amplifier as current. Draw a graph of the voltage difference between the two plates of the capacitor versus time. Mark the times when the amount of separated charge is increasing and when it's decreasing.

d. The transformer, diodes, and capacitor do a pretty good job of sending direct current through the amplifier, but there still tend to be periodic fluctuations in that current. To keep the current stable, the amplifier uses a regulating device. Just before the current enters the amplifier, it passes through an n-channel MOSFET. An electronic sensor measures the current through the amplifier and determines if that current is too high or too low. It then adjusts the charge on the gate of the MOSFET to increase or decrease the MOSFET's electrical resistance and lower or raise the current through the amplifier. If the sensor detects that the current is too high, should it increase or decrease the positive charge on the MOSFET's gate? Explain.

13.6. cordless microphone uses a 925-MHz carrier wave to carry sound information from a performer to the audio system of a theater.

a. The tank circuits in the microphone and in the theater's receivers have carefully been tuned to precisely the same resonant frequencies. Why is this adjustment important?

b. The frequencies of the waves emitted by the microphone include those slightly above and below 925 MHz. Explain.

d. Each receiver in the auditorium has two antennas oriented at right angles to one another. Why does this ensure that the receiver can detect the radio wave regardless of how the microphone's antenna is tipped?