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Resonance

Resonance. Resonance In a Tube. Sound waves in a tube can be looked at as standing waves of pressure, or displacement. Reflection in a Pipe. In a closed Pipe, High pressure reflects as High Pressure In an open Pipe, High pressure is reflected as Low Pressure

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Resonance

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  1. Resonance

  2. Resonance In a Tube • Sound waves in a tube can be looked at as standing waves of pressure, or displacement

  3. Reflection in a Pipe • In a closed Pipe, High pressure reflects as High Pressure • In an open Pipe, High pressure is reflected as Low Pressure • The frequencies required to produce resonance in an open pipe are not the same as those required to produce resonance in a closed pipe of the same length

  4. Closed Pipe • A closed pipe resonates when a standing wave is produced with a node on one end and an antinode on the other end • The distance between a node and an antinode is 1/4th of the wave length • The distance between antinodes is ½ of a wavelength

  5. Open Pipe • An Open Pipe resonates when there is either a node or antinode • The distance between consecutive nodes or antinodes is one half of a wavelength

  6. Calculation of Resonant Frequencies • The resonant frequencies in a pipe of known length can be calculated by knowing how many wavelengths are needed to resonate in a pipe • The first resonant wavelength will be equal to 4 times the length of the pipe (L) • The second will be ¾L, then 5/4L and so on.

  7. From Wavelength to Frequency • Recall that f = v/λ • If the first wavelength is 4L, the first frequency will be the speed of sound divided by 4L • Find the lowest frequency wave that can resonate in a closed pipe of length 8m

  8. Resonant Frequencies • For a closed pipe, the first resonance occurs when the length of the pipe is /4 meaning =4L • What is the next resonant frequency?

  9. 2nd resonant frequency in a closed pipe • f1 = v/4L • fn = (n+1)(f1)

  10. What is the first resonant frequency in a open pipe with respect to L • f1 = v/2L • f2 = v/L • f3 = 3v/2L • f4 = 2v/L • fn = n*f1

  11. Resonance in Musical Instruments • Musical instruments, unlike tuning forks resonate at multiple frequencies • The frequencies are the different resonant frequencies and the way that they interfere with each other gives the instrument its unique sound. • Each frequency sound wave will have a different intensity which makes the sound even more unique.

  12. Doppler Effect • A car honks its horn as it approaches a person standing on the side of the road. • The person hears a frequency of 430Hz when the car is approaching, and a frequency of 470Hz after the car is moving away from the observer. • What is the frequency of the horn? • What is the speed of the car?

  13. Resonance And Sound A Clarinet is a closed pipe roughly .75 m long. How long is the longest wavelength that will resonate in a clarinet? What is the frequency of the wave? What are the next two frequencies that will resonate?

  14. Resonance • A flute is an open pipe roughly .75 m long. What is the longest wavelength that will resonate in a flute? • What is the frequency? • What are the next two frequencies?

  15. Count the WavesFind the frequency in terms of L

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