1. AP Physics
Section 12-1 to 12-3
Sound Properties

2. Production of sound waves
A sound wave is a pressure variation that is transmitted through a medium (air, water, etc.).
Sound is a longitudinal wave with areas of high pressure (compressions) and low pressure (rarefactions). The wavelength is usually measured from compression to compression.

3. Speed of sound
Sound waves have a definite speed in air. The speed depends on air density, which in turn depends on temperature.
At standard temperature, 0°C, the speed of sound in air is:
vsound, 0°C = m/s
Speed increases by 0.6 m/s with every 1°C increase:
c = vsound = m/s + (0.6 m/s)T°C
What is the speed of sound at 37°C?
c =
= m/s
331.3 m/s + (0.6 m/s)(+37)
The speed of sound in other media is shown on p. 323.
Recall also that v = ƒ λ for all waves.

4. 344 m/s = 770 mph!

5. Hearing
Longitudinal sound waves travel through the ear canal to the eardrum. The vibrations of the eardrum move the three small bones called ossicles. The eardrum is attached to the malleus (hammer), which vibrates a lever-like bone called the incus (anvil). This bone is attached to the stapes (stirrup), which pushes on a membrane called the fenestra ovalis (oval window).

6. In the inner ear, the vibrations are transmitted to a fluid called the perilymph. This fluid is in the section of the inner ear called the cochlea. The membranes inside the spiral, bony part of the cochlea are lined with hair-like nerve cells that transmit signals to the cochlear nerve, and on to the brain.
The rest of the inner ear is used to inform the brain about the attitude, rotation, and linear motion of the head. This helps maintain our balance and visual focus.

7. Sound Intensity
Recall from Section 11–9 that the intensity of any wave front is the rate at which energy flows through a unit area.
The energy rate in joules per second is equivalent to power that we discussed before, and is therefore measured in watts. P
I =
area
Since sound propagates in three dimensions as a sphere, the area is given as the surface of a sphere, 4πr2, measured in square meters. P
Intensity
I =
Units:
W/m2
4πr2

8. Sound perception
The frequency of sound waves is perceived as pitch. The higher the frequency, the higher the pitch. Generally humans can not hear sounds below 20 Hz or above Hz. The frequency range decreases with age.
The amplitude of the sound wave is perceived as loudness. Humans can sense pressure differences as small as one-billionth of an atmosphere (2×10–5 Pa).
Sound level is measured on a logarithmic scale relative to the threshold of human hearing.
The threshold of human hearing at 1000 Hz has a pressure of 20 µPa (2×10–5 Pa) and a intensity rating of 1×10–12 W/m2.

9. Measuring loudness
The relative logarithmic scale is called the decibel scale.
LdB = 10log( I / I0)
where
I0 (1000 Hz) = 1×10–12 W/m2
threshold of human hearing
LdB = 10log( I / 1×10–12 W/m2)

10. turtle: 20–1000 Hz
cat: 30–50000 Hz
human: 20–20000 Hz
mouse: 1000– Hz
dog: 50–46000 Hz
dolphin: 1000– Hz

11. LdB = 85 dB LdB = 10log( I / I0) LdB/10 = log( I / I0)
Determining intensity from measured sound level
A sound engineer measures the sound level near freeway lanes at 85 dB. What is the sound intensity?
LdB = 85 dB
LdB = 10log( I / I0)
LdB/10 = log( I / I0)
10LdB/10 = I / I0
100.1LdB = I / I0
I = I0•10 0.1LdB
I = (1×10–12 W/m2)(108.5)
I = 3.2×10–4 W/m2
Recall that waves decrease in intensity by the square of the distance:
I ∝ 1 r2
To compare sound levels (decibels) at different distances, you have to convert to intensity, determine the different intensity farther away (or closer), then convert back to dB.

12. … still pretty darned loud!
A jet aircraft’s sound level at 30 m is a deafening 140 dB. What is the sound level 500 m away?
I1 = I0•10 0.1LdB =
(1×10–12 W/m2)(1014) = I1
102 W/m2 =
100 W/m2 I2 I1 =
r12
r22
r12
r22 I1
(30 m)2
(500 m)2
(100 W/m2) I2 = = I2 =
0.36 W/m2
LdB =
10log(0.36 W/m2 / 1×10–12 W/m2)
LdB =
116 dB
… still pretty darned loud!