- Accounting
- Aerospace Engineering
- Anatomy
- Anthropology
- Arts & Humanities
- Astronomy
- Biology
- Business
- Chemistry
- Civil Engineering
- Computer Science
- Communications
- Economics
- Electrical Engineering
- English
- Finance
- Geography
- Geology
- Health Science
- History
- Industrial Engineering
- Information Systems
- Law
- Linguistics
- Management
- Marketing
- Material Science
- Mathematics
- Mechanical Engineering
- Medicine
- Nursing
- Philosophy
- Physics
- Political Science
- Psychology
- Religion
- Sociology
- Statistics

HomeStudy GuidesPhysics

Menu

The Nature of Science and Physics

Kinematics

Introduction to One-Dimensional KinematicsDisplacementVectors, Scalars, and Coordinate SystemsTime, Velocity, and SpeedVideo: One-Dimensional KinematicsAccelerationMotion Equations for Constant Acceleration in One DimensionProblem-Solving Basics for One-Dimensional KinematicsFalling ObjectsGraphical Analysis of One-Dimensional Motion

Two-Dimensional Kinematics

Dynamics: Force and Newton's Laws of Motion

Introduction to Dynamics: Newton's Laws of MotionDevelopment of Force ConceptNewton's First Law of Motion: InertiaNewton's Second Law of Motion: Concept of a SystemNewton's Third Law of Motion: Symmetry in ForcesVideo: Newton's LawsNormal, Tension, and Other Examples of ForcesProblem-Solving StrategiesFurther Applications of Newton's Laws of MotionExtended Topic: The Four Basic Forces—An Introduction

Further Applications of Newton's Laws: Friction, Drag, and Elasticity

Uniform Circular Motion and Gravitation

Introduction to Uniform Circular Motion and GravitationRotation Angle and Angular VelocityCentripetal AccelerationCentripetal ForceFictitious Forces and Non-inertial Frames: The Coriolis ForceNewton's Universal Law of GravitationVideo: GravitationSatellites and Kepler's Laws: An Argument for Simplicity

Work, Energy, and Energy Resources

Introduction to Work, Energy, and Energy ResourcesWork: The Scientific DefinitionKinetic Energy and the Work-Energy TheoremGravitational Potential EnergyVideo: Potential and Kinetic EnergyConservative Forces and Potential EnergyNonconservative ForcesConservation of EnergyPowerWork, Energy, and Power in HumansWorld Energy Use

Linear Momentum and Collisions

Rotational Motion and Angular Momentum

Introduction to Rotational Motion and Angular MomentumAngular AccelerationKinematics of Rotational MotionVideo: Rotational MotionDynamics of Rotational Motion: Rotational InertiaRotational Kinetic Energy: Work and Energy RevisitedAngular Momentum and Its ConservationVideo: Angular MomentumCollisions of Extended Bodies in Two DimensionsGyroscopic Effects: Vector Aspects of Angular Momentum

Statics and Torque

Fluid Statics

Introduction to Fluid StaticsWhat Is a Fluid?DensityPressureVariation of Pressure with Depth in a FluidPascal's PrincipleGauge Pressure, Absolute Pressure, and Pressure MeasurementArchimedes' PrincipleVideo: BuoyancyCohesion and Adhesion in Liquids: Surface Tension and Capillary ActionPressures in the Body

Fluid Dynamics and Its Biological and Medical Applications

Introduction to Fluid Dynamics and Biological and Medical ApplicationsFlow Rate and Its Relation to VelocityBernoulli's EquationVideo: Fluid FlowThe Most General Applications of Bernoulli's EquationViscosity and Laminar Flow; Poiseuille's LawThe Onset of TurbulenceMotion of an Object in a Viscous FluidMolecular Transport Phenomena: Diffusion, Osmosis, and Related Processes

Temperature, Kinetic Theory, and the Gas Laws

Heat and Heat Transfer Methods

Thermodynamics

Introduction to ThermodynamicsThe First Law of ThermodynamicsThe First Law of Thermodynamics and Some Simple ProcessesIntroduction to the Second Law of Thermodynamics: Heat Engines and Their EfficiencyCarnot's Perfect Heat Engine: The Second Law of Thermodynamics RestatedApplications of Thermodynamics: Heat Pumps and RefrigeratorsEntropy and the Second Law of Thermodynamics: Disorder and the Unavailability of EnergyStatistical Interpretation of Entropy and the Second Law of Thermodynamics: The Underlying Explanation

Oscillatory Motion and Waves

Introduction to Oscillatory Motion and WavesHooke's Law: Stress and Strain RevisitedPeriod and Frequency in OscillationsSimple Harmonic Motion: A Special Periodic MotionVideo: Harmonic MotionThe Simple PendulumEnergy and the Simple Harmonic OscillatorUniform Circular Motion and Simple Harmonic MotionDamped Harmonic MotionForced Oscillations and ResonanceWavesSuperposition and InterferenceEnergy in Waves: Intensity

Physics of Hearing

- Define intensity, sound intensity, and sound pressure level.
- Calculate sound intensity levels in decibels (dB).

In a quiet forest, you can sometimes hear a single leaf fall to the ground. After settling into bed, you may hear your blood pulsing through your ears. But when a passing motorist has his stereo turned up, you cannot even hear what the person next to you in your car is saying. We are all very familiar with the loudness of sounds and aware that they are related to how energetically the source is vibrating. In cartoons depicting a screaming person (or an animal making a loud noise), the cartoonist often shows an open mouth with a vibrating uvula, the hanging tissue at the back of the mouth, to suggest a loud sound coming from the throat Figure 2. High noise exposure is hazardous to hearing, and it is common for musicians to have hearing losses that are sufficiently severe that they interfere with the musicians’ abilities to perform. The relevant physical quantity is sound intensity, a concept that is valid for all sounds whether or not they are in the audible range.

Intensity is defined to be the power per unit area carried by a wave. Power is the rate at which energy is transferred by the wave. In equation form,

$I=\frac{P}{A}\\$

, where $\displaystyle{I}=\frac{\left(\Delta{p}\right)^2}{2\rho{v}_{\text{w}}}\\$

.
Here Δ$\frac{mv^2}{2}\\$

) of an oscillating element of air due to a traveling sound wave is proportional to its amplitude squared. In this equation, Sound intensity levels are quoted in decibels (dB) much more often than sound intensities in watts per meter squared. Decibels are the unit of choice in the scientific literature as well as in the popular media. The reasons for this choice of units are related to how we perceive sounds. How our ears perceive sound can be more accurately described by the logarithm of the intensity rather than directly to the intensity. The

$\beta\left(\text{dB}\right)=10\log_{10}\left(\frac{I}{I_0}\right)\\$

, where Table 1. Sound Intensity Levels and Intensities | ||
---|---|---|

Sound intensity level β (dB) |
Intensity I(W/m^{2}) |
Example/effect |

0 | 1 × 10^{–12} |
Threshold of hearing at 1000 Hz |

10 | 1 × 10^{–11} |
Rustle of leaves |

20 | 1 × 10^{–10} |
Whisper at 1 m distance |

30 | 1 × 10^{–9} |
Quiet home |

40 | 1 × 10^{–8} |
Average home |

50 | 1 × 10^{–7} |
Average office, soft music |

60 | 1 × 10^{–6} |
Normal conversation |

70 | 1 × 10^{–5} |
Noisy office, busy traffic |

80 | 1 × 10^{–4} |
Loud radio, classroom lecture |

90 | 1 × 10^{–3} |
Inside a heavy truck; damage from prolonged exposure^{[2]} |

100 | 1 × 10^{–2} |
Noisy factory, siren at 30 m; damage from 8 h per day exposure |

110 | 1 × 10^{–1} |
Damage from 30 min per day exposure |

120 | 1 | Loud rock concert, pneumatic chipper at 2 m; threshold of pain |

140 | 1 × 10^{2} |
Jet airplane at 30 m; severe pain, damage in seconds |

160 | 1 × 10^{4} |
Bursting of eardrums |

One of the more striking things about the intensities in Table 1 is that the intensity in watts per meter squared is quite small for most sounds. The ear is sensitive to as little as a trillionth of a watt per meter squared—even more impressive when you realize that the area of the eardrum is only about 1 cm

Another impressive feature of the sounds in Table 1 is their numerical range. Sound intensity varies by a factor of 10

One more observation readily verified by examining Table 1 or using

$I=\frac{\left(\Delta{p}\right)^2}{2\rho{v}_{\text{w}}}\\$

is that 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, 10Table 2. Ratios of Intensities and Corresponding Differences in Sound Intensity Levels | |
---|---|

$\frac{I_2}{I_1}\\$ |
β_{2} – β_{1} |

2.0 | 3.0 dB |

5.0 | 7.0 dB |

10.0 | 10.0 dB |

$I=\frac{\left(\Delta{p}\right)^2}{\left(2\rho{v}_{\text{w}}\right)^2}\\$

. Using $\beta\left(\text{dB}\right)=10\log_{10}\left(\frac{I}{I_0}\right)\\$

.2. Enter these values and the pressure amplitude into

$I=\frac{\left(\Delta{p}\right)^2}{2\rho{v}_{\text{w}}}\\$

:$I=\frac{\left(\Delta{p}\right)^2}{2\rho{v}_{\text{w}}}=\frac{\left(0.656\text{ Pa}\right)^2}{2\left(1.29\text{ kg/m}^3\right)\left(331\text{ m/s}\right)}=5.04\times10^{-4}\text{ W/m}^2\\$

3. Enter the value for $\beta\left(\text{dB}\right)=10\log_{10}\left(\frac{I}{I_0}\right)\\$

. Calculate to find the sound intensity level in decibels:10 log_{10}(5.04 × 10^{8}) = 10(8.70)dB = 87 dB.

The ratio of the two intensities is 2 to 1, or:

$\frac{I_2}{I_1}=2.00\\$

.
We wish to show that the difference in sound levels is about 3 dB. That is, we want to show*β*_{2} − *β*_{1} = 3 dB.

$\log_{10}b-\log_{10}a=\log_{10}\left(\frac{b}{a}\right)\\$

.
2. Use the definition of $\beta_{2}-\beta_{1}=10\log_{10}\left(\frac{I_2}{I_1}\right)=10\log_{10}2.00=10\left(0.301\right)\text{ dB}\\$

Thus,*β*_{2} − *β*_{1} = 3.01 dB.

$\frac{I_2}{I_1}\\$

is given (and not the actual intensities), this result is true for any intensities that differ by a factor of two. For example, a 56.0 dB sound is twice as intense as a 53.0 dB sound, a 97.0 dB sound is half as intense as a 100 dB sound, and so on.50 dB: Inside a quiet home with no television or radio.

100 dB: Take-off of a jet plane.

- Intensity is the same for a sound wave as was defined for all waves; it is $I=\frac{P}{A}\\$, where
*P*is the power crossing area*A*. The SI unit for*I*is watts per meter squared. The intensity of a sound wave is also related to the pressure amplitude Δ*p*,$I=\frac{{\left(\Delta p\right)}^{2}}{2{\rho{v}}_{w}}\\$, where*ρ*is the density of the medium in which the sound wave travels and*v*_{w}is the speed of sound in the medium. - Sound intensity level in units of decibels (dB) is $\beta \left(\text{dB}\right)=\text{10}\log_{10}\left(\frac{I}{{I}_{0}}\right)\\$, where I
_{0}= 10^{–12}W/m^{2}is the threshold intensity of hearing.

- Six members of a synchronized swim team wear earplugs to protect themselves against water pressure at depths, but they can still hear the music and perform the combinations in the water perfectly. One day, they were asked to leave the pool so the dive team could practice a few dives, and they tried to practice on a mat, but seemed to have a lot more difficulty. Why might this be?
- A community is concerned about a plan to bring train service to their downtown from the town’s outskirts. The current sound intensity level, even though the rail yard is blocks away, is 70 dB downtown. The mayor assures the public that there will be a difference of only 30 dB in sound in the downtown area. Should the townspeople be concerned? Why?

- What is the intensity in watts per meter squared of 85.0-dB sound?
- The warning tag on a lawn mower states that it produces noise at a level of 91.0 dB. What is this in watts per meter squared?
- A sound wave traveling in 20ºC air has a pressure amplitude of 0.5 Pa. What is the intensity of the wave?
- What intensity level does the sound in the preceding problem correspond to?
- What sound intensity level in dB is produced by earphones that create an intensity of 4.00 × 10
^{−2}W/m^{2}? - Show that an intensity of 10
^{−12}W/m^{2}is the same as 10^{−16}W/m^{2}. - (a) What is the decibel level of a sound that is twice as intense as a 90.0-dB sound? (b) What is the decibel level of a sound that is one-fifth as intense as a 90.0-dB sound?
- (a) What is the intensity of a sound that has a level 7.00 dB lower than a 4.00 × 10
^{−9}W/m^{2}sound? (b) What is the intensity of a sound that is 3.00 dB higher than a 4.00 × 10^{−9}W/m^{2}sound? - (a) How much more intense is a sound that has a level 17.0 dB higher than another? (b) If one sound has a level 23.0 dB less than another, what is the ratio of their intensities?
- People with good hearing can perceive sounds as low in level as −8.00 dB at a frequency of 3000 Hz. What is the intensity of this sound in watts per meter squared?
- If a large housefly 3.0 m away from you makes a noise of 40.0 dB, what is the noise level of 1000 flies at that distance, assuming interference has a negligible effect?
- Ten cars in a circle at a boom box competition produce a 120-dB sound intensity level at the center of the circle. What is the average sound intensity level produced there by each stereo, assuming interference effects can be neglected?
- The amplitude of a sound wave is measured in terms of its maximum gauge pressure. By what factor does the amplitude of a sound wave increase if the sound intensity level goes up by 40.0 dB?
- If a sound intensity level of 0 dB at 1000 Hz corresponds to a maximum gauge pressure (sound amplitude) of 10
^{−9}atm, what is the maximum gauge pressure in a 60-dB sound? What is the maximum gauge pressure in a 120-dB sound? - An 8-hour exposure to a sound intensity level of 90.0 dB may cause hearing damage. What energy in joules falls on a 0.800-cm-diameter eardrum so exposed?
- (a) Ear trumpets were never very common, but they did aid people with hearing losses by gathering sound over a large area and concentrating it on the smaller area of the eardrum. What decibel increase does an ear trumpet produce if its sound gathering area is 900 cm
^{2}and the area of the eardrum is 0.500 cm^{2}, but the trumpet only has an efficiency of 5.00% in transmitting the sound to the eardrum? (b) Comment on the usefulness of the decibel increase found in part (a). - Sound is more effectively transmitted into a stethoscope by direct contact than through the air, and it is further intensified by being concentrated on the smaller area of the eardrum. It is reasonable to assume that sound is transmitted into a stethoscope 100 times as effectively compared with transmission though the air. What, then, is the gain in decibels produced by a stethoscope that has a sound gathering area of 15.0 cm
^{2}, and concentrates the sound onto two eardrums with a total area of 0.900 cm^{2}with an efficiency of 40.0%? - Loudspeakers can produce intense sounds with surprisingly small energy input in spite of their low efficiencies. Calculate the power input needed to produce a 90.0-dB sound intensity level for a 12.0-cm-diameter speaker that has an efficiency of 1.00%. (This value is the sound intensity level right at the speaker.)

3. 3.04 × 10

5. 106 dB

7. (a) 93 dB; (b) 83 dB

9. (a) 50.1; (b) 5.01 × 10

$\frac{1}{200}\\$

11. 70.0 dB

13. 100

15. 1.45 × 10

17. 28.2 dB

- Several "government agencies and health-related professional associations recommend that 85 dB not be exceeded for 8-hour daily exposures in the absence of hearing protection." ↵
- Several "government agencies and health-related professional associations recommend that 85 dB not be exceeded for 8-hour daily exposures in the absence of hearing protection." ↵