Sound Problems II
1. Two identical sources emit sound of frequency 2 kHz. They are separated by 25.7 cm.
(a) What type of interference is heard at a distance of 5 m away along the axis joining the speakers?
(b) I now increase the frequency of both speakers. Find the next frequency for which I will hear destructive interference.
(c) Now return to 2 kHz. What, if anything, can I do to get the opposite type of interference as in part (a)?
2. . Suppose I have two speakers, separated by 5.09 m, each emitting an 800 Hz sound in air, and Vincent listens at a point 30 m away as shown (not to scale).
(a) Assume that the speakers are in phase–that is, they both emit a peak at the same time. What will I hear, constructive or destructive interference?
(b) Now I move the bottom speaker vertically. At what speaker separation will I hear the other type of interference from part (a)?
(c) Suppose I double the frequency of the speakers, what will I hear for the two separations in (a) and (b) above?
(d) Find three other frequencies at which I will hear constructive interference from the speaker separation in part (a). Find three other frequencies at which I will hear destructive interference in the same situation.
3. The apparatus shown in the diagram can be built with ordinary plastic pipes. Sound enters the tube at the top and can go either left or right, going around and leaving the tube at the bottom. The right hand C shaped section can be slid left or right. Assume that we have a 3 kHz sound.
(a) As I slide the tube out, what will I hear?
(b) Suppose I start with a maximum sound and pull the right hand tube out 5.71 cm. Describe what I hear: a loud or quiet sound?
4. Consider a string of length L with nodes at each end.
(a) Draw the lowest 3 frequency standing wave patterns and complete the other items.
Pattern (Sketch) # of l in L l frequency
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(b) Now label each picture with successive Nodes [N] and Antinodes [A]. for example, the lowest pattern would be NAN.
(c) Use the NAN notation to list the first 8 patterns. What is the general relationship between the length of the string and the wavelengths that allow the ends of the string to be nodes?
(d) Now suppose I touch my finger lightly at the center of the string, at L/2. Which of the above patterns could appear on your touched string? What does this tell you about the series of overtones that result from a harmonic played in this way compared to the series of overtones produced by simply plucking the string? (This difference is key to the “bell like” tone you get when playing a harmonic note like this on a stringed instrument.)
5. Consider a tube open at one end and closed at the other. The closed end will be a displacement node, and the open end will be (approximately) a displacement antinode.
Sketch and write in NAN notation the first 6 patterns that could be observed. What is the general relationship between the length of the tube and the wavelengths that “fit” in the tube in the proper way? Determine each of these resonant frequencies.
What are the similarities/differences between the harmonic series produced by the tube and that produced by the vibrating string?
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