38 Interference: Review and homework

Important Terms

• interference
• (principle of) superposition
• constructive interference
• destructive interference
• phase
• in phase
• completely out of phase
• beats
• beat frequency
• difference tone
• nodal line
• antinodal line
• point source (a.k.a. monopole)
• dipole
• quadrupole

Review Questions

1. What happens when two waves or pulses meet? What happens at the moment the waves/pulses meet? What happens after they meet?
2. Is it possible to combine two sounds and end up with a sound that is quieter than either sound alone? Explain.
3. Explain how active noise canceling headphones work. Explain why a microphone is an essential component of active noise canceling systems.
4. What is phase? How is phase related to interference?
5. If you point two sources that are playing the same pure tone at each other, what happens? Explain.
6. What are beats? What causes beats?
7. What is a difference tone? What causes a difference tone?
8. Compare and contrast beats and difference tone.
9. Explain how beats can be used to tune musical a musical instrument.
10. Explain how it’s possible for sources that are in phase with each other to destructively interfere with each other.

Numericals

1. Two pulses travel toward each other on a string at a speed of 1 m/s, as shown in the diagram. What does the string look like 10 seconds later? What does the string look like 20 seconds later? (You can check your answer here).
   

   

2. Two pulses travel toward each other on a string at a speed of 1 m/s, as shown in the diagram. What does the string look like 10 seconds later? What does the string look like 20 seconds later? (You can check your answer here).
   

   

3. When one trumpet plays a 440 Hz tone while another trumpet plays a 442 Hz tone at about the same loudness, the listener hears a single tone with a pulsating loudness. What is the frequency of the pitch the listener hears? How often does the loudness of the combined sound pulse? How much time passes between one “wah” and the next?
4. Two loudspeakers 2.3 meters apart are pointed at each other outdoors in an open field. Both play the same pure tone. A person walking from one speaker to the other notices that there are some locations where he hears a loud tone and other locations where he hears almost nothing.
   • Explain why there are “dead spots” and “hot spots.”
   • Explain briefly how the “dead spots” could be eliminated (but still have the tone be heard).
   • If the distance between one dead spot and the next is 40 cm, calculate the frequency of the sound coming through the speakers.
5. A pure tone of 440.00 Hz is played with an equally loud pure tone of 440.01 Hz.
   • What will you hear? Explain.
   • If you hear beats, calculate how many seconds will elapse between one beat and the next. If you hear a difference tone, calculate the frequency of the difference tone.
   • List the frequencies of all the distinct pitches you hear.
6. A pure tone of 1800 Hz is played with an equally loud pure tone of 2100 Hz.
   • What will you hear? Explain.
   • If you hear beats, calculate how many seconds will elapse between one beat and the next. If you hear a difference tone, calculate the frequency of the difference tone.
   • List the frequencies of all the distinct pitches you hear.
7. Two speakers, S1 and S2, are 120 cm apart. Point A is located somewhere along the midline between the two speakers. Point B is 160 cm from Speaker 1 and 200 cm away Speaker 2. The speakers are set up in phase and play a constant tone with a wavelength of 16 cm.
   • Will there be a “hot spot”, “dead spot” or something else at point A? Explain.
   • Will there be a “hot spot”, “dead spot” or something else at point B? Explain.
8. Repeat the previous question for speakers producing 10 cm waves that are completely out of phase.
9. Two audio speakers are 120 cm apart. Point A is located somewhere along the midline between the two speakers. Point B is 160 cm from Speaker 1 and 200 cm away Speaker 2. Both speakers play music and are in phase.
   • Which will a listener at point A hear (circle one): music, almost nothing, or music with missing frequencies? Explain.
   • Which will a listener at point B hear (circle one): music, almost nothing, or music with missing frequencies? Explain.
   • Calculate two frequencies that will be missing from the music at point B. (Hint: Find the wavelengths first!)
   • What would the answers to this question be if the speakers were completely out of phase (rather than in phase)?

Explorations

1. In Audacity, record (or generate) almost any sound you want in one track and duplicate the track. (Duplicate is in the Edit menu). Select a portion of one of the tracks by clicking and dragging and invert your selection. (Invert is on the “Effect”menu). Play the entire recording to hear the result. To see what’s happening with the waves, zoom in.
2. In Audacity, generate a tone. For best results, choose a tone around 500 Hz that lasts for about 20 seconds. In another track, generate what Audacity calls a “chirp” that slowly from about 50 Hz below the constant tone you made to a few Hertz above. (Choose linear interpolation of frequency for most dramatic results). Listen as the character of the sound changes. Audacity’s chirp allows you to generate a sound that has increasing or decreasing frequency over time.
3. In Audacity, generate a tone. For best results, choose a tone around 500 Hz that lasts for about 20 seconds. In another track, generate what Audacity calls a “chirp” that slowly from about 50 Hz above the constant tone you made to about 1000 Hertz above.