# Sound

## Sound Intensity and Sound Level


### Section Key Terms


### Amplitude, Loudness and Energy of a Sound Wave

In a quiet forest, you can sometimes hear a single leaf fall to the ground. But in a traffic jam filled with honking cars, you may have to shout just so the person next to you can hear .The loudness of a sound is related to how energetically its source is vibrating. In cartoons showing a screaming person, the cartoonist often shows an open mouth with a vibrating uvula (the hanging tissue at the back of the mouth) to represent a loud sound coming from the throat.  shows such a cartoon depiction of a bird loudly expressing its opinion.
A useful quantity for describing the loudness of sounds is called sound intensity. In general, the intensity of a wave is the power per unit area carried by the wave. Power is the rate at which energy is transferred by the wave. In equation form, intensity I is
where P is the power through an area A. The SI unit for I is W/m2. The intensity of a sound depends upon its pressure amplitude. The relationship between the intensity of a sound wave and its pressure amplitude (or pressure variation Δp) is
where ρ is the density of the material in which the sound wave travels, in units of kg/m3, and v is the speed of sound in the medium, in units of m/s. Pressure amplitude has units of pascals (Pa) or N/m2. Note that Δp is half the difference between the maximum and minimum pressure in the sound wave.
We can see from the equation that the intensity of a sound is proportional to its amplitude squared. The pressure variation is proportional to the amplitude of the oscillation, and so I varies as (Δp)2. This relationship is consistent with the fact that the sound wave is produced by some vibration; the greater its pressure amplitude, the more the air is compressed during the vibration. Because the power of a sound wave is the rate at which energy is transferred, the energy of a sound wave is also proportional to its amplitude squared.

### The Decibel Scale

You may have noticed that when people talk about the loudness of a sound, they describe it in units of decibels rather than watts per meter squared. While sound intensity (in W/m2) is the SI unit, the sound intensity level in decibels (dB) is more relevant for how humans perceive sounds. The way our ears perceive sound can be more accurately described by the logarithm of the intensity of a sound rather than the intensity of a sound directly. The sound intensity level β is defined to be
where I is sound intensity in watts per meter squared, and I0 = 10–12 W/m2 is a reference intensity. I0 is chosen as the reference point because it is the lowest intensity of sound a person with normal hearing can perceive. The decibel level of a sound having an intensity of 10–12 W/m2 is β = 0 dB, because log10 1 = 0. That is, the threshold of human hearing is 0 decibels.
Each factor of 10 in intensity corresponds to 10 dB. For example, a 90 dB sound compared with a 60 dB sound is 30 dB greater, or three factors of 10 (that is, 103 times) as intense. Another example is that if one sound is 107 as intense as another, it is 70 dB higher.
Since β is defined in terms of a ratio, it is unit-less. The unit called decibel (dB) is used to indicate that this ratio is multiplied by 10. The sound intensity level is not the same as sound intensity—it tells you the level of the sound relative to a reference intensity rather than the actual intensity.

### Solving Sound Wave Intensity Problems


### Practice Problems


### Hearing and Voice

People create sounds by pushing air up through their lungs and through elastic folds in the throat called vocal cords. These folds open and close rhythmically, creating a pressure buildup. As air travels up and past the vocal cords, it causes them to vibrate. This vibration escapes the mouth along with puffs of air as sound. A voice changes in pitch when the muscles of the larynx relax or tighten, changing the tension on the vocal chords. A voice becomes louder when air flow from the lungs increases, making the amplitude of the sound pressure wave greater.
Hearing is the perception of sound. It can give us plenty of information—such as pitch, loudness, and direction. Humans can normally hear frequencies ranging from approximately 20 to 20,000 Hz. Other animals have hearing ranges different from that of humans. Dogs can hear sounds as high as 45,000 Hz, whereas bats and dolphins can hear up to 110,000 Hz sounds. You may have noticed that dogs respond to the sound of a dog whistle which produces sound out of the range of human hearing.
Sounds below 20 Hz are called infrasound, whereas those above 20,000 Hz are ultrasound. The perception of frequency is called pitch, and the perception of intensity is called loudness.
The way we hear involves some interesting physics. The sound wave that hits our ear is a pressure wave. The ear converts sound waves into electrical nerve impulses, similar to a microphone.
 shows the anatomy of the ear with its division into three parts: the outer ear or ear canal; the middle ear, which runs from the eardrum to the cochlea; and the inner ear, which is the cochlea itself. The body part normally referred to as the ear is technically called the pinna.
The outer ear, or ear canal, carries sound to the eardrum protected inside of the ear. The middle ear converts sound into mechanical vibrations and applies these vibrations to the cochlea. The lever system of the middle ear takes the force exerted on the eardrum by sound pressure variations, amplifies it and transmits it to the inner ear via the oval window. Two muscles in the middle ear protect the inner ear from very intense sounds. They react to intense sound in a few milliseconds and reduce the force transmitted to the cochlea. This protective reaction can also be triggered by your own voice, so that humming during a fireworks display, for example, can reduce noise damage.
 shows the middle and inner ear in greater detail. As the middle ear bones vibrate, they vibrate the cochlea, which contains fluid. This creates pressure waves in the fluid that cause the tectorial membrane to vibrate. The motion of the tectorial membrane stimulates tiny cilia on specialized cells called hair cells. These hair cells, and their attached neurons, transform the motion of the tectorial membrane into electrical signals that are sent to the brain.
The tectorial membrane vibrates at different positions based on the frequency of the incoming sound. This allows us to detect the pitch of sound. Additional processing in the brain also allows us to determine which direction the sound is coming from (based on comparison of the sound’s arrival time and intensity between our two ears).

### Check Your Understanding


### Section Summary

1. The intensity of a sound is proportional to its amplitude squared.
2. The energy of a sound wave is also proportional to its amplitude squared.
3. Sound intensity level in decibels (dB) is more relevant for how humans perceive sounds than sound intensity (in W/m2), even though sound intensity is the SI unit.
4. Sound intensity level is not the same as sound intensity—it tells you the level of the sound relative to a reference intensity rather than the actual intensity.
5. Hearing is the perception of sound and involves that transformation of sound waves into vibrations of parts within the ear. These vibrations are then transformed into neural signals that are interpreted by the brain.
6. People create sounds by pushing air up through their lungs and through elastic folds in the throat called vocal cords.

### Key Equations


### Concept Items


### Critical Thinking


### Problems


### Test Prep Multiple Choice


### Test Prep Short Answer


### Test Prep Extended Response


### References

Nave, R. Vocal sound production—HyperPhysics. Retrieved from http://hyperphysics.phy-astr.gsu.edu/hbase/music/voice.html