interference and beats
TRANSCRIPT
Interference and Beat
Application to Piano
• 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 - ωt + ϕ)
SPHERICAL WAVES
CONSTRUCTIVE INTERFERENCE
• 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 -ωt + ϕ)
• 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
Δd= d2 – d1= (n+ 0.5) λ
DESTRUCTIVE INTERFERENCE
• 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(ϖt)cos(∆ωt)
can be used with the following quantities
and
BEATS
• 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.
BEATS AND PIANO NOTES
• Question 1:
Two piano keys produce the frequencies of 262 Hz (C) and 330 Hz (G). What is the beat frequency?
BEATS AND PIANO NOTES
• Answer:
330 Hz- 262 Hz= 68 Hz
BEATS AND PIANO NOTES
• Question 2:
Why don't we hear beats when different keys on the piano are played at the same time?
BEATS AND PIANO NOTES
• 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.
BEATS AND PIANO NOTES
• 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?
BEATS AND PIANO NOTES
• Answer:
300 Hz- 294 Hz= 6 Hz
In 10 seconds, there will be 60 beats.
BEATS AND PIANO NOTES
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!
WORKS CITED