constructive interference results when destructive interference results when two special interference patterns are the and the

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1 Interference and Sound Last class we looked at interference and found that constructive interference results when destructive interference results when two special interference patterns are the and the More on Sound Random sound waves have frequencies which vary randomly and are difficult to study. The sounds we will examine for the remainder of the unit are sounds which maintain their frequency for an extended length of time. Pleasing sounds or sound with "quality' results from interference of sound waves which are related mathematically. (analyzed later in this note) Sounds that do not have the "right" mathematical relation and whose frequency is maintained, produce patterns which are not pleasing to the ear. Two pure frequencies that differ slightly will produce "beats" of constructive and destructive interference. We would hear constructive interference as a sound and we would hear destructive interference as a sound. So the "beats" heard represent a noticeable changing of the amplitude of sound. bf = f 2 f 1 The number of beats produced is based on the differences between the two frequencies creating the original sounds. Humans can hear up to 7 beats per second. 25. Two tuning forks of frequencies 512 Hz and 518 Hz are sounded at the same time. a. Describe the resultant sound. b. Calculate the beat frequency. 26. A 440 Hz tuning fork is sounded at the same time as a 437 Hz tuning fork. How many beats will be heard in 3.0 s? 27. A trumpet player sounds a note on her trumpet at the same time as middle C is played on a piano. She hears 10 beats over 2.0 the piano s middle C has been tuned to 256 Hz, what are the possible frequencies of the note she is sounding? 28. A string on an out of tune piano is struck at the same time as a 440 Hz tuning fork is sounded. The piano tuner hears 12 beats s. He then slightly increases the tension in the string in order to increase the pitch of the note. Now he hears 14 beats in 4.0 s. a. What was the original frequency of the string on the out of tune piano? b. Is the piano more or less in tune after he tightens the string? Explain. 25. (b) 6.00 Hz beats Hz or 261 Hz 28. (a) 443 Hz 1

2 Interference and Sound Waves A sound wave for a single note would have a very predictable shape Noise that is annoying to the ear would have a very erratic shape to its characteristic wave. Notice in the following musical instruments that a main wave is easy to identify for each instrument. To understand this, one must have an understanding of interference. Add the following two waves 2

3 Sound waves interfere all the time. Most times this interference is a result of Reflection Reflection of waves as seen through a single pulse fixed end reflection free end reflection reflection when changing mediums less dense and more dense Standing waves are more likely to occur during reflection because Reflection of sound waves occurs in any musical instrument. The length of the wave is often determined largely by the length of the instrument!!! The strings The pitch of a vibrating string depends on four things. The mass of the string: more massive strings vibrate more slowly. On steel string guitars, the strings get thicker from high to low. On classical guitars, the size change is complicated by a change in density: the low density nylon strings get thicker from the E to B to G; then the higher density wire wound nylon strings get thicker from D to A to E. The frequency can also be changed by changing the tension in the string using the tuning pegs: tighter gives higher pitch. This is what what you do when you tune up. The frequency also depends on the length of the string that is free to vibrate. In playing, you change this by holding the string firmly against the fingerboard with a finger of the left hand. Shortening the string (stopping it on a higher fret) gives higher pitch. Finally there is the mode of vibration, which is a whole interesting topic on its own. For more about strings and harmonics, see Strings and standing waves < The strings themselves make hardly any noise: they are thin and slip easily through the air without making much of disturbance and a sound wave is a disturbance of the air. An electric guitar played without an amplifier makes little noise, and an acoustic guitar would be much quieter without the vibrations of its bridge and body. In an acoustic guitar, the vibration of the string is transferred via the bridge and saddle to the top plate body of the guitar. good for horns and woodwinds 3

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5 Air columns produced during the reflection of air in woodwind and brass instruments Open air columns Closed air columns csa.gc.ca/eng/educators/resources/neemo/sound/speech.asp Air columns are excellent examples of how sound is generate in many instruments and how the quality of sound is developed. To fully understand air columns, one has to have an understanding of reflection, interference and resonance Reflection fixed and free end If the wave is continuous, the reflective wave will with the rest of the wave. This reflected wave will have the same and as the continuous wave creating the conditions for a special interference pattern a Development of Air columns 5

6 What 2 changes can be made to produce different air columns? What changes are depicted in the pictures below? 6

7 What changes are depicted in this picture? Air columns are also can be analyzed along the quality of its sound. A specific length of an air column would have unique frequencies which produce the pictures depicted. As argued in previous lessons, the various harmonic frequencies could exist for that given length. Questions 29. A narrow plastic pipe is almost completely submerged in a graduated cylinder full of water, and a tuning fork is held over its ope end. The pipe is slowly raised from the water. An increase in loudness of the sound is heard when the pipe has been raised 17 cm an again when it has been raised 51 cm. a. Determine the wavelength of the sound produced by the tuning fork. b. If the pipe continues to be raised, how far from the top of the pipe will the water level be when the next increase in loudness is heard? 30. The first resonance length of an air column, resonating to a fixed frequency, is 32 cm. a. Determine the second and third resonance lengths, if the column is closed at one end. b. Determine the second and third resonance lengths, if the column is open at both ends. 31. The third resonance length of a closed air column, resonating to a tuning fork, is 95 cm. Determine the first and second resonanc lengths. 32. The second resonance length of an air column, open at both ends and resonating to a fixed frequency, is 64 cm. Determine the fi and third resonance lengths. 33. A particular organ pipe, open at both ends, needs to resonate in its fundamental mode with a frequency of 128 Hz. The organ has been designed to be played at a temperature of 22 C. a. How long does the organ pipe need to be? b. If this pipe is closed at one end by a stopper, at what fundamental frequency will it resonate? 34. An air column, open at both ends, resonates with a fundamental frequency of 256Hz. Determine the frequencies of its first and second overtones (second and third harmonics). 35. A bugle is essentially a 2.65 m pipe that is open at both ends. The temperature of the room is C. 20 a. Determine the lowest frequency note that can be played on a bugle. b. Determine the next two higher frequencies that will produce resonance. 36. A trombone is playing F (87.3 Hz) as its fir harmonic. A trombone functions as an air column that is open at both ends. a. Determine the second harmonic. b. If the speed of sound is 344 m/s, what I the length of the tubing being used? Why would this note be difficult to play? 29. (a) 68 cm (b) 85 cm 30. (a) 96 cm, 160 cm (b) 64 cm, 96 cm cm, 57 cm cm 33. (a) 1.34 m (b) 64 Hz Hz, 768 Hz 35. (a) 64.9 Hz (b) 130 Hz, 195 Hz 36. (a) 175 Hz (b) 1.97 m 7

8 A narrow plastic pipe is almost completely submerged in a graduated cylinder full of water, and a tuning fork is held over its open end. The pipe is slowly raised from the water. An increase in loudness of the sound is heard when the pipe has been raised 17 cm and again when it has been raised 51 cm. a. Determine the wavelength of the sound produced by the tuning fork. b. If the pipe continues to be raised, how far from the top of the pipe will the water level be when the next increase in loudness is heard? 8

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