Interference and Beats

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  1. 1. Spherical waves are three dimensional waves. Spherical waves oscillate in space and time. However, their amplitudes remain constant over any spherical surface centered on the source. This allows us to write the wave function of a spherical wave as S(r, t) = sm (r)cos (kr - t + )
  2. 2. Locations where two waves are perfectly in phase Determined to occur whenever the path difference is an integer multiple of the wavelength Resultant waves can be determined using the formula S(d, t)= 2sm(d)cos (kd -t + )
  3. 3. Locations where two waves are perfectly out of phase Determined to occur when one path is an integer multiple of wavelengths and the other is a half integer multiple In other words, whenever d= d2 d1= (n+ 0.5)
  4. 4. Two waves with slightly different frequencies have variation of amplitude which results in a beat. When the frequency difference between two sound waves is very large then we hear two distinct tones rather than one that varies in intensity To determine the resultant wave the equation Stotal(0, t)=2smcos(t)cos(t) can be used with the following quantities and
  5. 5. The following slide is a video using piano notes to explain the concepts of consonance, dissonance, beats, and interference Review: All musical notes have their own unique frequencies.
  6. 6. Question 1: Two piano keys produce the frequencies of 262 Hz (C) and 330 Hz (G). What is the beat frequency?
  7. 7. Answer: 330 Hz- 262 Hz= 68 Hz
  8. 8. Question 2: Why don't we hear beats when different keys on the piano are played at the same time?
  9. 9. Answer: In order to hear beats, two interfering sound waves must have a difference in frequency of 7 Hz or less. No two keys on the piano produce such a frequency.
  10. 10. Question 3: If a tuning fork with a frequency of 300 Hz is played simultaneously with a note with a frequency of 294 Hz (D). How many beats will be heard over a period of 10 seconds?
  11. 11. Answer: 300 Hz- 294 Hz= 6 Hz In 10 seconds, there will be 60 beats.
  12. 12. Hawkes Et Al. Physics for Scientists and Engineers: An Interactive Approach. Vol. 1. Vancouver: U of British Columbia, n.d. Print. Thank you for watching!