Acoustics and Fourier Transform

Transcription

1 AFT Acoustics and Fourier Transform 1. A Hamming filter is used to compute FFT (Fast Fourier Transform) plots in the AFT experiment. What is the reason for using such a filter? 2. Briefly describe what is meant by undersampling when acquiring a periodic signal for FFT? 3. Briefly describe the phenomenon of acoustic beats? 4. What is the ratio of two frequencies (f 1 and f 2 ) that are 3 octaves apart? 5. Calculate the velocity of sound in a gas in which the waves of wavelength 50 cm and 50.5 cm produce 6 beats per second. 6. Consider a string of length L stretched between two supports that is plucked like a guitar or violin string. a. Draw the first four harmonic wave patterns (fundamental, first, second and third overtone). b. Write down their corresponding wavelengths in terms of string length L. c. Write down the corresponding frequencies in terms of the fundamental frequency f Consider standing waves in two tubes of length L. One tube is open at both ends (open tube) and one tube is closed at one end (closed tube). a. What is the criteria for the wave amplitude at a closed end? b. What is the criteria for the wave amplitude at an open end? c. What is the fundamental wavelength for the open tube? d. What is the fundamental wavelength for the closed tube? 8. Consider the plots (a) and (b). Briefly discuss the FWHM of the FFTs of the two waveforms.

2 CEO Coupled Electrical Oscillator Consider an electrical circuit containing a resistor (R), inductor (L), capacitor (C), switch (K), and battery, as shown in the figure. When the switch is set to the battery, the capacitor becomes charged to Q o. When the switch is moved to the inductor, the LRC circuit is completed through the inductance and resistance. As the capacitor loses its charge it generates a current (I). Let q(t) be the charge on the capacitor at time t. K C L R 1. Write down the potential difference across the capacitor (C). 2. Write down the potential difference across the resistor (R). 3. Write down the voltage required to overcome the back e.m.f. in the inductance (L). 4. Show that L di dt + RI + q C = Show that d2 q dq + 2k + dt2 dt ω2 q = 0, using 2k = ( R ) and L ω2 = ( 1 ). LC 6. Using the trial solution q = Qe αt, solve for α. 7. Derive the equation for R that determines the onset of critical damping. 8. For L= H and C=1.80 μf, what is the maximum value of resistance so that the circuit produces underdamped oscillations? Round off the answer. 9. If the resistance in an underdamped LRC oscillator is decreased by a factor of two, from R=2R o to R=R o, how much does the oscillation amplitude change at time t=2l/r o? 10. Discuss how the beating effect in a coupled oscillator system is different than beating of acoustic waves.

3 FUEL Fuel Cell and Solar Cell 1. What is meant by the term bandgap of a material? Discuss the major material classification of conductors, insulators and semiconductors with respect to their bandgap energies. 2. Briefly describe a direct bandgap semiconductor and an indirect bandgap semiconductor. 3. In the Lab apparatus, what type of bandgap does the solar cell have? 4. Briefly explain the working principle of a photovoltaic (PV) solar cell? 5. What material would make a solar cell that has a much higher efficiency than silicon? 6. List some methods to obtain hydrogen for industrial-size fuel cells. Discuss their advantages and disadvantages? 7. Compare the typical efficiencies of: a fuel cell; an automobile engine; and a natural gas electrical power plant. 8. Suppose that you left 10 cm 3 of hydrogen gas in the Lab apparatus for the weekend. If a candle produces 80 W of heat power, how long would a candle have to burn to release the same amount of combustion energy in the leftover hydrogen?

4 HALL Hall Effect 1. Briefly explain why the 4-wire resistance setup eliminates the errors due to contact resistances, thus accurately measuring the resistance of the silicon wafer region of interest. 2. When measuring the resistivity of a semiconductor, what are the crucial dimensions that must be measured when using the following techniques: a. using the rectangular geometry from the HALL Lab instructions; b. using the geometry of the van der Pauw technique. Discuss the main difference in the techniques. 3. Write down an equation for the current density (J) in terms of current (I) and cross sectional area (A), including the units. 4. Consider a Hall bar in the shape of a rectangular semiconductor of width (w) and thickness (d), under the influence of a magnetic field (B) and electrical current (I). Derive an equation for the electric field that pushes the charge carriers to one side of the Hall bar. 5. Consider a Hall bar experiment using a germanium wafer of thickness d=1 mm, having a current of I=1.00 ma and a magnetic field of B=1.00 tesla, which gives a Hall voltage of V H =1.00 V. a. What is the value of the carrier density? b. Using a value for the mobility of electrons in Ge, what is the value of the resistivity in units of Ωcm? 6. List a useful application of the Hall effect. 7. Explain the term Fermi energy (E F )? Draw individual energy band diagrams (only with conduction and valence bands) to show the position of E F in n- and p-type semiconductors.

5 RUBY Spectroscopy of Ruby Fluorescence 1. Compare plasma emission with fluorescence by indicating what is common and what is different for the two light emitting mechanisms. 2. Describe the ruby crystal structure and its elements. Which element is responsible for the fluorescence and what does it replace? 3. Briefly explain population inversion in a lasing medium. What does the lifetime of an energy level have to do with it? 4. Briefly describe the differences between spontaneous emission and stimulated emission. 5. What percentage of visible light is passed through a 3 mm thick window made of fused silica (SiO 2 )? What percentage of light is passed through a 0.1 mm thick clear Mylar (polyethylene) plastic sheet? Which transmits more light? Assume absorption is zero. Compute and explain. 6. In designing a laser diode (LD), what elements are required to produce blue light? 7. Depending on the relative positions of a lens and an object, the image produced by a convex lens could be real, imaginary or no image. Draw ray diagrams for: a. the object is further than the focal length; b. the object is at the focal length; and c. the object is less than the focal distance. With the help of these three diagrams, comment on the real/imaginary images.

6 SOL Speed of Light 1. The light emitted from a conventional source is said to be incoherent. Why? 2. Light traveling in a vacuum experiences changes as it enter a different medium. What changes and what does not change? Briefly explain. 3. What is the speed of light in a sapphire (Al 2 O 3 ) crystal? 4. List and briefly describe the important parts of a fiber optics (FO) cable. 5. Describe total internal reflection? 6. What is the value of the critical angle for total internal reflection in a diamond crystal? 7. Suppose you are measuring the speed of light in air by splitting a laser beam into two beams that are traveling different distances and you measure the time delay between the two beams. If you did the same experiment in a vacuum, what would be the percentage difference in the computed speed of light? 8. Consider that the refractive index of a diamond crystal can be measured in a speed of light experiment. How much longer would it take a laser beam to travel in a diamond of thickness d= cm versus that same distance in air? Round off the answer.