Name_____________________
P109 Exam 1, Fall 2003
Instructions: Answer all of the following questions. Put your answers in the space provided in the exam. You may look at anything you bring. Each problem is worth 2 points, unless otherwise indicated, for a total possible of 50 points. P.S. Please remember to include units for all answers requiring them.
1. You have an oscilloscope and a function generator. Suppose you want to make a ________ wave with a peak-to-peak amplitude of ________ Volts and frequency of ________ Hz. You are given the following scale settings:
Vertical scale: _______ Volts/div
Horizontal scale: _______ msec/div
a) How many vertical divisions will you need? Include fractional ones.
b) How many horizontal divisions will you need to put one cycle in? Include fractional ones.
2. (3 points) Make the wave in #1 with the given equipment and show it to the lab person. Time limit: 4 minutes
A mass hanging from a spring oscillates with amplitude of 3 cm. Questions 3-4 refer to this mass.
3. Suppose you measure the time it takes for 17 cycles to complete as 16.84 seconds.
a) (1point) Please calculate the period of oscillation.
b) (1point) Please calculate the frequency of oscillation.
4. You calculate the theoretical value for the period as 0.84 seconds. Does your measurement agree with theory? Please use guidelines set in class to determine this.
5. Suppose we halve the amount of mass hanging from the spring. Select the correct choice.
A. The period of oscillation will double.
B. The period of oscillation will halve.
C. The period of oscillation will not change.
D. None of the above.
6. Sound intensity is proportional to 1/r2. State the two key reasons for this relationship.
7. Suppose the speed of sound in some warm room is 34700 cm/s. What is the temperature of the room?
Suppose you have a harmonic series of sine waves with a fundamental of 113 Hz. The amplitudes are set so that the fundamental has amplitude 1/5 Volts, the second harmonic 1/6 Volts, the third harmonic 1/7 Volts, the fourth 1/8 Volts, the fifth 1/9 Volts, the sixth 1/10 Volts and so forth up until the nth harmonic with an amplitude of 1/(n+4) Volts. Switch out all odd harmonics. Answer questions 8-10 regarding this situation.
8. Write down the first three harmonics of the new harmonic series. Indicate missing ones if any.
9. The wave resulting from the addition of the new harmonic series is a
A. sawtooth wave.
B. square wave.
C. triangle wave.
D. none of the above.
10. Calculate the period of the resulting wave (after switching out the odds) in ms.
11. The frequency difference between the 5th and 12th harmonic is f12 – f5 = 490 Hz. What is the 4th harmonic, f4?
12. A vibrating string has a fundamental standing wave at 130 Hz when the length of the string is 57 cm. At what length will it have a fundamental standing wave if you quadruple the fundamental frequency to 520 Hz? Assume the string material and tension on the string stay the same.
A string is fixed at both ends as shown below. You pluck it (or use a gizmo) so as to excite only the 3rd harmonic. Questions 13-17 refer to this situation.
13. Sketch the 3rd harmonic in the figure below.
14. Suppose the length of the string is 1.65 meters. What is the wavelength of this wave?
15. You measure the period of the 3rd harmonic as 3.30 msec. What is the frequency for this wave?
16. Find the fundamental frequency for this wave.
17. Calculate the speed of this wave on the string.
18. A sound signal has a period of 0.4 seconds, peak-to-peak amplitude of 5 V and one complete cycle as shown below. Draw the sound signal for a total duration of 2.0 seconds (including the shown cycle). What is the frequency of the signal?
Questions 19-20 refer to the figures below.
19. Select the true statement.
A. The period of A is shorter than the period of B.
B. The frequency of A is the same as the frequency of B.
C. The frequency of A is smaller than the frequency of B.
D. None of the above.
20. The peak-to-peak amplitude of B compared to A is:
A. larger
B. smaller
C. the same
21. A sound pulse travels 560 mm with a speed of 345 m/s. Find the time it takes to cover the said distance in ms.
Questions 22 and 23 refer to the following figures.
22. Select the true statement.
A. #1 is 180 degrees out of with #2
B. #1 is 270 degrees out of phase with #2
C. #1 has negative amplitude of #2
D. both A and C
E. both B and C
F. none of the above
23. Select the true statement.
A. #2 is 180 degrees out of with #3
B. #2 is 90 degrees out of phase with #3
C. #2 has negative amplitude of #3
D. both A and C
E. both B and C
F. none of the above
24. (3 points) Add the two signals below and sketch the resultant wave.
Extra Credit (3 points):
Suppose you measure the speed of sound in a room (called #1) as v1 = 346.5 m/s. You then proceed to another room (called #2) and measure the ratio of the temperatures of #1 to #2 as T1/T2 = 6/5. What is the speed of sound in room #2, v2?