1. Sound
Chapter 13

2. Sound Waves
Sound waves are areas of alternating high and low molecular densities.
Longitudinal
Caused by vibrations
Compression-areas of high molecular density
Rarefactions-areas of low molecular density

3. Speed of Sound
The speed of sound depends on the medium in which it propagates.
Solids Liquids Gases
Hot Cold
(Fast to Slow)

4. Human Hearing Audible Sounds
Humans can hear frequencies (known as pitch) between 20 Hz and 20,000 Hz
Frequencies higher than we can hear…
Ultrasonic
Frequencies lower than we can hear…
infrasonic

5. Sound Characteristics
Pitch-results from differences in frequency
The higher the frequency, the higher the pitch
Don’t directly observe wavelength
Infrasonic and Ultrasonic
Loudness-results from amplitude
Logarithmic relationship between intensity and perceived loudness.
Increasing intensity by 10 times only results in a doubling of perceived loudness.

6. Intensity Rate at which energy flows Inverse square relationship
Units of W/m2
We will assume the sound spreads in all directions equally so the area we are dealing with is the surface area of a sphere (4πr2).

7. Intensity and Human Hearing
Intensity ranges:
Threshold of Hearing to Threshold of Pain
1.0 x W/m2 to 1 W/m2
This is a large range:
Logarithmic scale compresses this range
Use Decibel levels

8. The Decibel Scale Hearing damage starts at 85dB
For each 10dB step, the intensity increases by 10 times and the perceived loudness increases by 2 times.

9. Examples
Calculate the intensity of the sound waves from an electric guitar’s amplifier at a distance of 5.0 m when its power output is equal to each of the following values:
0.25 W
0.50 W
2.0 W
If the intensity of a person’s voice is 4.6 x 10-7 W/m2 at a distance of 2.0 m, how much sound power does that person generate?
The power output of a tuba is 0.35 W. At what distance is the sound intensity of the tuba 1.2 x 10-3 W/m2?

10. The Doppler Effect
The shift in perceived frequency of a wave due to relative motion between the source and the observer.
Observable in both sound (pitch) and light (red and blue shifts)
As the sound approaches - higher f
As sound leaves - lower f
Occurs as either listener or source is moving

11. Forced Vibrations and Natural Frequency
Forced Vibration – a vibration that occurs when a periodic force causes an object to vibrate at a particular frequency
Singing
Natural Frequency – the frequency an object will vibrate at when given a one time force
Depends on shape and material of object

12. Resonance
The amplified wave that occurs when a forced vibration on an object matches the natural frequency of the object.
Makes the wave progressively larger.
Swing set example

13. Music
Different notes have different mathematical relationships between their frequencies.
Specific frequency combinations are considered pleasant (harmony) and others unpleasant (dissonance).
2:1 = Octave (C to the next C)
5:4 = Major Third (C to E)
4:3 = Perfect Forth (C to F)
3:2 = Perfect Fifth (C to G)

14. Instruments
The sound produced by the vibration of a piece of the instrument (string, reed, lips) is amplified and shaped through resonance by the rest of the instrument.
Standing waves are produced within the instrument at certain frequencies depending on either the properties of the string or the shape and size of the instrument.

15. Strings Physically, wavelength is restricted to certain values.
To change those values, the length of the string needs to be changed (different keys on a piano, different finger placements on a guitar)
The longest wavelength on the string is the sound you hear as the note being played and is called the fundamental or first harmonic.

16. Wavelengths
The higher frequency vibrations are played simultaneously and are called overtones. Therefore, the next longest wavelength will be the second harmonic or first overtone.

17. Frequencies
Since all of the waves are on the same medium and travel at the same speed, there will be a pattern to the frequency as well as the wavelength.

18. Closed Pipe Node on one end, antinode on the other.
Diagrams help with determining wavelength pattern.

19. Wavelengths and Frequencies
Where n=1, 3, 5…
Closed pipes have only odd harmonics

20. Open Pipes
The same as the closed pipe, however there is an anti-node at each end for molecular movement and a node at each end for pressure variance.

21. Wavelengths and Frequencies

22. Beats
Beats are a result of two waves with close, but not identical frequencies.
A pattern of constructive and destructive interference forms creating a warbling sound.
Useful for tuning instruments.
Beat frequency is equal to the difference between the two component frequencies.

23. Timbre
The unique combination of intensities of fundamental and overtone frequencies that makes instruments sound different when playing the same note.
Trumpet
Flute
Cello

24. Examples
What is the fundamental frequency of a 0.2 m long organ pipe that is closed at one end, when the speed of sound in the pipe is 352 m/s?
A flute is an open pipe. The length is the flute is approximately 66.0 cm. What are the first three harmonics of a flute when all keys are closed, making the length of air equal to the length of the flute? Use 340 m/s for the speed of sound.
What is the fundamental frequency of a guitar string when the speed of waves on the string is 115 m/s and the effective string lengths are as follows:
70.0 cm
50.0 cm
40.0 cm
A violin string that is 50.0 cm in length has a fundamental frequency of 440 Hz. What is the speed of the waves on this string?