EXAM I -- WAVES
All work on this exam must be your own. You may use a calculator and a 3"X5" card of equations. Clearly indicate your final answer for each question. You are required to do ALL of the multiple choice problems, and 4 of the 5 long-answer problems.
Section 1: Multiple choice. No partial credit will be given for this section. Circle only one answer for each question.
1) If the frequency of a traveling wave is increased by a factor of three, but the medium remains unchanged,
a) the amplitude increases to 3 times the original amplitude.
b) the amplitude decreases to 1/3 the original amplitude.
c) the wavelength increases to 3 times the original wavelength.
d) the wavelength decreases to 1/3 the original wavelength.
2) Which of the following is not true of a standing wave in a string?
a) Energy is transmitted from one end of the string to the other.
b) Kinetic energy is converted to potential energy and back again as the string vibrates.
c) It is made up of two otherwise identical waves moving in opposite directions through the string.
d) The nodes of the wave remain in the same position.
3) A wave travels through a string. Which of the following properties is at a maximum for the part of the string that is at its maximum displacement.
a) the speed of the wave
b) the speed of that part of medium
c) the potential energy stored in that part of the medium
d) all of the above
4) A wire is cut into two pieces. One is slightly longer than the other. If the two pieces of wire are to play the same note, the longer one should have
a) a higher tension than the shorter one.
b) a lower tension than the shorter one.
c) the same tension as the shorter one.
5) When the displacement wavefunction (describing the displacement of molecules in a sound wave) is minimum, the pressure wavefunction is
6) Which of the following could describe a standing wave in a pipe open at both ends?
d) More than one answer is correct.
7) A vibrating guitar string emits a tone simultaneously with one from a 500 Hz tuning fork. If a beat frequency of 5 Hz results, what is the frequency of vibration of the string?
a) 100 Hz
b) 495 Hz
c) 505 Hz
d) More than one answer could be correct.
8) The speed of sound is faster in warm air than in cool air, so a sound wave passing from warm air to cool air will
a) increase in frequency.
b) decrease in frequency.
c) not change in frequency.
Section 2: Problems and questions. Partial credit will be given for this section. Show ALL WORK and JUSTIFY all answers. Be sure your answers include UNITS where appropriate.
11) An organ pipe, 1 m long, is open at the left end, and stopped at the right end.
a) Sketch the first three modes of standing waves in this pipe. Be sure to label the axes on all sketches, and label the wavelength on at least one of the sketches.
b) What is the frequency of the third mode?
c) If the organ pipe is unstopped, what happens to the pitch? Why?
13) a) How fast would you need to move toward a musical instrument for the pitch to be 6% different (a semitone or "half-step" in music) from the pitch the musician hears?
b) Would the pitch you hear in part (a) be higher or lower than the pitch the musician hears?
c) Explain what causes shock waves or sonic booms (a sketch may be helpful).
14) A 440 Hz sound wave travels in air. The maximum displacement of the air molecules is 1X10-6 m.
a) Find the wavelength of this sound wave.
b) Find the wave number (k) and the angular frequency (w ) of this sound wave.
c) Give the equation describing this sound wave, including units (you may assume zero phase).
15) A 660 Hz point source of sound has an intensity of 0.5 mW/m2 at a distance of 2 m. assume the sound is emitted isotropically.
a) What is the intensity at a distance of 10 m?
b) What is the sound level in dB at a distance of 10 m?
c) What is the displacement amplitude of the sound wave at a distance of 10 m?
speed of sound in air at 20C and 1 atm = 343 m/s,
density of air same conditions = 1.21 kg/m3