Physics of Sound & Music:Day 05

Diffraction, Beats & The Doppler Effect

WarmUp Response: Beat It!

What does the beat frequency mean? For example, if the beat frequency is 3 Hz, what is happening 3 times per second?~42% → Amplitude of combined wave increases and

then decreases

~8% → Combined tone gets loud then soft

~8% → Waves go in-and-out of phase

~33% → Confused or answered a different question

“Beat frequency is the number of beats per second related to the difference in frequencies of both beats. One of 40 and one of 30 would be a BF of 10”

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WarmUp Response: Beat It!

“The beat frequency means the number of beats per second, so a beat frequency of 3 hz would mean that the difference between the two interacting frequencies creates a 3 hz beat pattern.”

“A)The beat frequency means that the amplitude of the resultant wave increases and decreases 3 times per second.”

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WarmUp Response: Beat It!

If the beat frequency was zero, what would this tell you about the two tones you are combining?~58% → They have the same frequency

~25% → They are in-phase, const. interfere

~33% → They are out-of-phase, dest. interfere

~8% → Had misconceptions or bad terminology

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WarmUp Response: Beat It!

“If the beat frequency was zero this would mean that the two tones that I am combining are canceling each other out.”

“B)If the beat frequency was zero then the two tones that are being combined consist of one negative and one positive.”

“b)If the beat frequency was zero, the two tones would be the same frequency and they would be completely out of phase, canceling each other out. There would be no movement in and out of phase.”

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Adding Waves: Beats

• From superposition and interference you have seen waves added several times now.

• Addition of waves is so important because (again)all waves can be treated as combinations of many simple sine waves, each with a different frequency.

• A famous example of this is the phenomena of beats.• When two sound waves with very slightly different

frequencies are combined we hear only one tone, which has "beats" in it.

• Musicians use beats to tune instruments, often using harmonics, which we will discuss soon.

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When the air inside a flute heats up, the speed of sound in the air changes. This causes the frequency of the flute’s sound to increase as well.

Suppose we had one flute with cool air in it and one with hot air.

How much hotter would the air in the second one need to be in order to produce a 5 Hz beat frequency when they both play a middle C?

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The Doppler Effect

• If either the observer or the source of a sound moves through the air the frequency will be affected.

• Commonly known because of hearing cars pass you on the street, it is easy to confuse the volume of the sound with the frequency of the sound.

• The effect is not symmetric. That is, it matters whether the observer or the source is moving.

Observer moving: Source moving:

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0oS v

f fS

0s

Sf f

S v

speed of

soundspeed of source

speed of observer

How many of the following are true?• The waves move faster at A than at B and C.• The waves move faster at C than at A and B.• The frequency of sound is highest at A.• The frequency of sound is highest at B.• The frequency of sound is highest at C.

A) 1 of them

B) 2 of them

C) 3 of them

D) 4 of them

E) All of them

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A violin player rides on her skateboard (like you do) practicing her middle C (f = 261.6 Hz). If she is riding towards you at 10 m/s (fast!), what frequency would you hear from her violin?

A) ƒ = 269.2 Hz

B) ƒ = 269.5 Hz

C) ƒ = 271.6 Hz

D) ƒ = 287.8 Hz

What if you were on the board and she were still?

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Sonic Booms

• If the source moves faster than the speed of sound, the sounds it creates do not spread out in front of it.

• Instead, all the sounds over a long period combine to create a shockwave called a sonic boom.

• All the sounds you would have heard as the plane approached you arrive at once! Very loud indeed.

(sometimes occurring when a plane goes supersonic is a Prandtl-Glauert Condensation Cloud)

• Whip-cracks and thunder are other examples of shockwaves similar to sonic booms.

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Ultrasonics and Infrasonics

• Used in dozens of applications, ultrasound is sound that is much higher frequency than humans can hear.

• From imaging babies, to shattering kidney stones, to drilling through ceramic, ultrasound can do much!

• Sonoluminescence and tiger pistol shrimp are two extreme, but cool, examples.

• Infrasonic sound (below 20 Hz) has fewer applications and its effects on people are not well-understood.

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Reading:

Thursday (9/6) → 3.1 – 3.2

Tuesday (9/11) → 3.3 – 3.5

Thursday (9/13) → Quiz on Ch. 1-3

Notes:

Homework #2 due today by 5 PM

Homework #3 due Friday by 5 PM:Ch. 2: Q: 7, 9, 15, 17 + Ch. 3: P: 1 + Theory

WarmUp due Wednesday by 10 PM

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