1. Sound

2. Production of sound Sound waves are longitudinal
Air molecules vibrate in SHM producing compressed areas (high density) and expanded or rarefacted areas (low density)
Crest – high density
Trough – low density

3. Characteristics
Frequencies that the human ear can respond to are called “audible”.
Range from 20 to Hz
Infrasonic – frequencies below 20 Hz
Ultrasonic – frequencies above Hz
The “pitch” of a sound is determined by its frequency.

4. Sound waves move out in a 3-D sphere from the source.
Wave fronts
(compression)
ray

5. The speed of a sound wave depends on the medium through which it moves.
The frequency is set by the source of the sound. If the speed
changes due to a change in medium it is the wavelength (λ)
that will change.

6. Speed of Sound preAP -- the speed of sound changes by 0.6 m/s for
The speed of sound depends on the medium.
As density of the medium increases, speed increases.
As temperature of the medium increases, speed increases
And will decrease as the temp decreases
The speed at 0oC is 331 m/s for dry air
preAP the speed of sound
changes by 0.6 m/s for
each degree from 0o C

7. Doppler Effect
Motion of either the source or the listener causes a “perceived” change in frequency (pitch).
If the motion is toward the listener, pitch increases
If the motion is away from the listener, pitch decreases.
Remember: speed does not change in a constant medium
Motion causes waves
to “spread” : λ is greater
so f is lower.
Motion causes waves
to “bunch” : λ is shorter
so f is higher.

8. preAP only - Doppler Calculation
v = velocity of sound in air
vs = velocity of source
vo = velocity of observer or detector
f = frequency of source (emitted freq)
f ' = apparent frequency (detected freq))
Upper signs = moving toward Lower signs = away

9. A truck’s horn blows at a frequency of 500 Hz
A truck’s horn blows at a frequency of 500 Hz. A boy on a bicycle moves toward the truck at 10 m/s. What is the apparent frequency heard by the boy? Assume sound travels at 340 m/s.
f ’ = 500 Hz (340 m/s + 10 m/s)
(340 m/s – 0 m/s)
f ’ = 500 Hz ( 350/340) = 515 Hz
Notice = the objects are moving toward each other so the wave fronts
are “bunched” together and the pitch (perceived frequency)
goes up.

10. Sound Intensity I = intensity (W/m2) P = Power of source (watts)
Sound intensity is the power of a sound wave per unit area.
I = intensity (W/m2)
P = Power of source (watts)
r = distance from
source (m)
Sound waves move out in a 3-D sphere from the source so area is 4pr2.
Intensity is an inverse square relationship.

11. preAP only - Relative Intensity a ratio of the sound intensity to threshold of hearing
I = intensity (W/m2)
Io = W/m (threshold of hearing)
 = decibels (dB)

12. Comparison of Sound Intensities
The inverse square relationship means a sound that is twice as far away is one-fourth as intense, and one that is three times as far away is one-ninth as intense.
Comparing intensity of a sound at two distances:
The comparison reduces to the intensities and the radii since the power
is constant (from the same source) and 4π is also constant.

13. A horn blows with constant power
A horn blows with constant power. A child 8 m away hears a sound of intensity W/m2. What is the intensity heard by his mother 20 m away? What is the power of the source?
Given: I1 = 0.60 W/m2; r1 = 8 m, r2 = 20 m
I1 r12 = I2 r22
I2 = W/m2

14. From the previous example: What is the power of the source?
Given: I1 = 0.60 W/m2; r1 = 8 m I2 = W/m2 ; r2 = 20 m
P = 7.54 W

15. Human Hearing
Your ability to hear a sound depends on (a) the intensity and (b) frequency.
Threshold of hearing = 1.0 x W/m2
Threshold of pain = 1.0 x 100 W/m2

16. Relative Intensity
When a sound is given a “decibel” rating, the intensity of that sound
is being compared to the threshold of hearing.

17. Concepts (log scale) A 10 dB increase = 10 times the intensity
10x the pressure on your ear
A 10 dB increase = twice the loudness
double the volume to your hearing
Example: One sound is at 40 dB and the other at 60 dB. This is a difference of 20 or 2 x 10. The intensity is 102 greater (100x) and the loudness is 2x greater (twice as loud).

18. Mechanics of the human ear

19. Comparing your perception of the sound with the physical measurements
Sensory effects Physical property
Loudness
Pitch
Quality
Intensity
Frequency
Waveform

20. Remember units! Frequency -- Hertz (cycles/sec) Period -- seconds
Wavelength -- meters
Wave speed -- m/s
Sound Intensity -- W/m2
Relative sound intensity -- decibels (dB)

21. Resonance
Every system has a natural frequency at which it will oscillate.
If a force causes vibration at that frequency, the object will respond by vibrating.
This is called resonance or resonance matching

22. Standing waves on strings
When a string of a set length vibrates at its lowest frequency (fundamental) a standing wave is produced with nodes at each end.
As the frequency increases, more waveforms are produced
1st harmonic or fundamental
frequency: L = (1/2)
What frequency will produce this
wave?
f1 = (v/2L)
2nd harmonic (1st overtone): L =(2/2) 
f2 = 2(v/2L) or 2 (f1)
3rd harmonic (2nd overtone): L = (3/2)
f3 = 3(v/2L) or 3 ( f1)

23. Resonance and Fundamental Frequency in air columns (tubes)
Open ends have an antinode
Closed or fixed ends have a node
fundamental frequency is lowest frequency possible (called the 1st harmonic)
use length of pipe (or string) to calculate wavelength or vice versa
use speed of sound = 343 m/s, if not given

24. Resonance in Open Pipes
General equation for frequency:
fn = n(v/2L)
n = all integers
Note: open pipes have the same frequency pattern as strings. The lowest frequency is ½ of a full wave but with antinodes at each open end.
Stringed instruments act
as fixed ends with nodes
at each end.

25. Resonance in closed-end pipes
1st harmonic or fundamental frequency:
L = (1/4)
What frequency will produce this wave?
f1 = (v/4L)
3rd harmonic (1st overtone): L =(3/4) 
f3 = 3(v/4L) or 3 x f1
5th harmonic (2nd overtone): L = (5/4)
f5 = 5(v/4L) or 5 x f1
General equation for frequency: fn = n(v/4L)
n = odd integers

26. Beats
Beats occur due to interference patterns between sound waves of slightly different frequencies. Hear alternating loud and soft sounds.
Sounds with frequencies separated by 7 Hertz or less will produce beats that can be detected by the human ear.