Transcript
Page 1: Interference and Beats

Interference and Beat

Application to Piano

Page 2: Interference and Beats

• 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

Page 3: Interference and Beats

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)

Page 4: Interference and Beats

• 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

Page 5: Interference and Beats

• 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

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• 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

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• 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

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• Answer:

330 Hz- 262 Hz= 68 Hz

BEATS AND PIANO NOTES

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• Question 2:

Why don't we hear beats when different keys on the piano are played at the same time?

BEATS AND PIANO NOTES

Page 10: Interference and Beats

• 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

Page 11: Interference and Beats

• 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

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• Answer:

300 Hz- 294 Hz= 6 Hz

In 10 seconds, there will be 60 beats.

BEATS AND PIANO NOTES

Page 13: Interference and Beats

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


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