1. Sound
Chapter 26

2. Sound
Sound is a mechanical wave which is created by a vibrating object.
The vibrations of the particles in sound waves are best described as longitudinal.
Sound waves are longitudinal waves because particles of the medium through which the sound is transported vibrate parallel to the direction which the sound moves.
A vibrating string can create longitudinal waves as depicted in the animation above.

3. Sound is a Pressure Wave
The result of the longitudinal vibrations is the creation of compressions and rarefactions within the air.
The compressions are regions of high air pressure.
The rarefactions are regions of low air pressure.

4. Sound Properties and Their Perception
When a pressure wave reaches the ear, a series of high and low pressure regions impinge upon the eardrum.
The pitch of a sound wave is related to its frequency.
The frequency of a wave is measured as the number of complete back-and-forth vibrations of a particle of the medium per unit of time.
The units of frequency are Hertz. 1 Hertz = 1 vibration/second.
The human ear can hear in the 20 Hz -20,000 Hz range.
Any sound with a frequency below the audible range of hearing (i.e., less than 20 Hz) is known as an infrasound
Any sound with a frequency above the audible range of hearing (i.e., more than Hz) is known as an ultrasound.

5. Sound Properties and Their Perception
The loudness of a sound is related to its amplitude/energy.
The amount of energy which is transported past a given area of the medium per unit of time is known as the intensity of the sound wave.
The scale for measuring intensity is the decibel scale (dB).
The faintest sound which the human ear can detect is known as the threshold of hearing ( 0 dB).
Sounds with a decibel rating above the threshold of pain (130 dB) cause damage to the ear.
The same sound will not be perceived to have the same loudness to all individuals, age and frequency can influence how a sound is perceived.
The human ear's tendency to amplify sounds having frequencies in the range from 1000 Hz to 5000 Hz, sounds with these intensities seem louder to the human ear.

6. Resonance
Nearly all objects, when hit or struck or plucked or strummed or somehow disturbed, will vibrate.
The frequency or frequencies at which an object tends to vibrate with when hit, struck, plucked, strummed or somehow disturbed is known as the natural frequency of the object.
Resonance - when one object vibrating at the same natural frequency of a second object forces that second object into vibrational motion.

7. Resonance – Tacoma Narrows Bridge
The Tacoma Narrow Bridge was a bridge that experienced a dramatic wind induced structural collapse.
The wind forced the bridge to oscillate at its natural frequency causing increasingly larger oscillations.

8. Interference of Pressure Waves in a Tube
Standing waves are produced on strings and in tubes in musical instruments creating sound waves of various frequencies.
Open End Air Column
Closed End Air Column

9. Harmonics on a String
A string of length, L, can support several different frequencies. These frequencies are known as harmonic frequencies, or merely harmonics.
L = ½ l
L = l
L = 3/2 l

10. Harmonics - Open End Air Column
An open tube must have anti-nodes at each end.
L = ½ l
L = l
L = 3/2 l

11. Harmonics - Closed End Air Column
A closed tube must have a node at the closed end and a anti-node at the open end.
L = 1/4 l
L = 3/4 l
There are only odd harmonics for a closed-end tube because of the node on the closed end.
L = 5/4 l

12. Problem Solving – Standing Waves on a String or in a Pipe/Tube

13. Speed of Sound
The speed of sound depends on temperature and the material that the sound is traveling through.
Sound travels fastest through solids and slowest through gasses: vsolids > vliquids > vgases
The temperature dependence of the speed of a sound wave through air is approximated by the following equation:
v = 331 m/s + (0.6 m/s/C)*T
At room temperature (20 degrees Celsius), sound travels about 343 m/s.
Light travels through air at a speed of approximately m/s; this is nearly times the speed of sound.
The wave equation, v = f * l, can be used to relate the speed, frequency and wavelength of sound waves.

14. Beats
Beats are the periodic and repeating fluctuations heard in the intensity of a sound when two sound waves of very similar frequencies interfere with one another.
The beat frequency refers to the rate at which the volume is heard to be oscillating from high to low volume. The beat frequency is always equal to the difference in frequency of the two notes which interfere to produce the beats.

15. Sound Questions Sound is a _____________ wave.
As the temperature of air increases, the speed of sound ___________.
A tremor can be felt before it is heard, what does this suggest of about the relative speed of sound waves in different materials?
What beat frequency results when two tuning forks are struck, one has at 625 Hz and the other at 621 Hz?
Why do we see lighting before we hear thunder?
Pitch is related to what property of sound waves?
Loudness is related to what property of sound waves?
What happened to the Tacoma Narrows Bridge?

16. More Sound Questions
9) Specify the number of wavelengths on string a, b, c and d and write an equation that relates wavelength, l, and string length, L, for each. 10) If the string above is 0.5 m, find the wavelength and frequency of a sound wave produced by each string. a b c d

17. Sources
Conceptual Physics by Paul Hewitt