Intensity of a Spherical Wave

intensity = the rate at which energy flows through a unit area perpendicular to the direction of wave motion

Units =

I=𝑃

4𝜋𝑟 2

PracticeThe intensity of the sound from an explosion is 0.10 W/m2 at a distance of 1000 m. Find the intensity of the sound at a distance of 1500 m.

At what distance would the intensity be doubled?

Both intensity and frequency determine which sounds are audible

Relative IntensityHuman perception of loudness is approximately logarithmic

decibel (dB) = a dimensionless unit that describes the ratio of two intensities of sound (the reference intensity is usually the threshold of hearing)

Converting between dB and I

Examples

PracticeThe sound level changes from 40 dB to 80 dB. By how much does the intensity change?

Vibrations

• Forced vibrations occur from contact; the object is forced to have the same frequency

• Sympathetic vibrations occur if the object has the same natural frequency

• An object’s natural frequency is the frequency of unforced vibrations

Resonance

resonance = a phenomenon that occurs when the frequency of a force applied to a system matches the natural frequency of vibration of the system, resulting in a large amplitude of vibration

Tacoma Narrows1940

The Human Ear• Sound wave vibrations are transferred: eardrum -> bones in

middle ear -> cochlea• Sound waves resonate at different spots in the basilar

membrane -> impulses to nerve cells