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 4𝜋 𝑟 2

Practice The intensity of the sound from an explosion is 0 Practice The 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 Intensity Human 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 X0 dB= 10 −12+X W m 2 Examples 40 dB= 10 −12+4 = 10 −8 W m 2 90 dB= 10 −12+9 = 10 −3 W m 2

Practice The sound level changes from 40 dB to 80 dB Practice The 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 Narrows 1940

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