1. Physics 7E
Prof. D. Casper

2. Admin All lecture slides (Chapters 12, 14, 15) have been posted
Midterm one week from today
Will post draft of formula sheet over weekend
Note: no homework due next Thursday (Chapter 16 HW is due November 3, available on MasteringPhysics now)

3. Chapter 16: Sound and Hearing
You should learn:
How to describe a sound wave in terms of particle displacements or pressure fluctuations
How to calculate the speed of sound in different materials
How to calculate the intensity of a sound wave
What determines the particular frequencies produced by an organ or a flute
How resonance occurs in musical instruments
What happens when sound waves from different sources overlap
How to describe what happens when sound waves of slightly different frequencies overlap
Why the pitch of a siren changes as it moves past you

4. What is Sound? Sound is a longitudinal mechanical wave
Direction of displacement is same as direction wave travels
Can occur in solids, liquids or gases
Audible frequencies: 20 Hz – 20 kHz
“Ultrasound”: higher than 20 kHz
“Infrasound”: lower than 20 Hz

5. Two Descriptions
Disturbance can be described by displacement in position of particles (air molecules) from their equilibrium positions
Disturbance can be described by the difference in pressure from the equilibrium value
High pressure: particles displaced toward location
Low pressure: particles are displaced away from location
Displacement and pressure waves are ¼ cycle (90 degrees, 𝜋/2 radians) out of phase

6. Relating Displacement and Pressure
The Bulk Modulus B of a material is defined in terms of the pressure change resulting from a volume change: 𝑝=−𝐵 𝑑𝑉 𝑉 The fractional volume change is 𝑑𝑉 𝑉 = 𝑦 2 − 𝑦 1 𝑆 𝑆 Δ𝑥 → 𝜕𝑦 𝜕𝑥 So the pressure change is related to the displacement by: 𝑝=−𝐵 𝜕𝑦 𝜕𝑥

7. Sinusoidal Pressure Wave
The sinusoidal (displacement) wave: 𝑦 𝑥,𝑡 =𝐴 cos⁡(𝑘𝑥−𝜔𝑡) is equivalent to the sinusoidal (pressure) wave: 𝑝 𝑥,𝑡 =𝐵𝑘𝐴 sin⁡(𝑘𝑥−𝜔𝑡)

8. Sound as Perceived Properties of sound as perceived: Pitch Loudness
Mostly frequency
Also depends on amplitude
Loudness
Not linear with amplitude
Sound quality or timbre

9. Sound Speeds
In general: 𝑣 𝑤𝑎𝑣𝑒 = 𝑟𝑒𝑠𝑡𝑜𝑟𝑖𝑛𝑔 𝑓𝑜𝑟𝑐𝑒 𝑡𝑒𝑟𝑚 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 𝑡𝑒𝑟𝑚 for example: 𝑣 𝑠𝑡𝑟𝑖𝑛𝑔 = 𝐹 𝜇 in air or other fluid, use bulk modulus B: 𝑣 𝑠𝑜𝑢𝑛𝑑 = 𝐵 𝜌 in solids, use Young’s modulus Y: 𝑣 𝑠𝑜𝑢𝑛𝑑 = 𝑌 𝜌

10. Wavelength
The speed of sound in air is 344 m/s What is the wavelength of the sound with the frequency of middle-C on a piano (262 Hz)?
0.38 m
0.65 m
0.76 m
1.3 m
9.0 m

11. Sound Intensity and Decibels
Intensity = Power per unit area
But perceived sound tends to vary logarithmically
Define the sound level in decibels:
𝛽= 10 dB log 𝐼 𝐼 0
+10 dB = a factor of 10 increase in intensity
+20 dB = a factor of 100 increase in intensity
Can be relative (𝐼 and 𝐼 0 are any two intensities)
Can be absolute ( 𝐼 0 corresponds to threshold of hearing, 10 −12 W/ m 2 )

12. How many dB?
If one trumpet player has a sound level of 50 dB, what is the sound level of four trumpet players?
50 dB
51 dB
54 dB
56 dB
200 dB

13. Absolute Sound Levels