Sound Intensity and Vibrations

Sound Intensity

▪ Rate that energy flows through a given area– Intensity = (ΔE/Δt) = P .

area area

Intensity is Power ÷ area watt/m2

Equation for the area of a circle = 4πr2

Sound Intensity

▪ Vibrating objects do work on the air as they push against the molecules.

▪ Intensity is the rate of energy flow through an area.– What is “rate of energy flow”

called?▪ E/t is called power (P).

– Since the waves spread out spherically, you must calculate the area of a sphere. How?▪ A = 4r2

– So, what is the equation for intensity?

Sound Intensity

▪ SI unit: W/m2

▪ This is an inverse square relationship.– Doubling r reduces intensity by ¼.– What happens if r is halved?▪ Intensity increases by a factor of 4.

Intensity and Decibels

▪ An intensity scale based on human perception of loudness is often used.

▪ The base unit of this scale is the bel. More commonly, the decibel (dB) is used.– 0.1 bel = 1 dB,1 bel = 10 dB, 5 bels = 50 dB, etc.

– The lowest intensity humans hear is assigned a value of zero.

▪ The scale is logarithmic, so each increase of 1 bel is 10 times louder.– An increase in intensity of 3 bels is 1 000 times louder.

Click below to watch the Visual Concept.

Visual Concept

Human Hearing

Threshold of Hearing

Source IntensityIntensity

Level# of Times

Greater Than TOH

Threshold of Hearing (TOH) 1*10-12 W/m2 0 dB 100

Rustling Leaves 1*10-11 W/m2 10 dB 101

Whisper 1*10-10 W/m2 20 dB 102

Normal Conversation 1*10-6 W/m2 60 dB 106

Busy Street Traffic 1*10-5 W/m2 70 dB 107

Vacuum Cleaner 1*10-4 W/m2 80 dB 108

Large Orchestra 6.3*10-3 W/m2 98 dB 109.8

Walkman at Maximum Level 1*10-2 W/m2 100 dB 1010

Front Rows of Rock Concert 1*10-1 W/m2 110 dB 1011

Threshold of Pain 1*101 W/m2 130 dB 1013

Military Jet Takeoff 1*102 W/m2 140 dB 1014

Instant Perforation of Eardrum 1*104 W/m2 160 dB 1016

Intensity

▪ Measured in decibels– Relative intensity- relating the intensityof a given sound to the intensity

a the threshold of hearing

– Dimensionless because it is a comparison unit

Audible Sounds

▪ The softest sound humans can hear is called the threshold of hearing.– Intensity = 1 10-12 W/m2 or zero dB

▪ The loudest sound humans can tolerate is called the threshold of pain.– Intensity = 1.0 W/m2 or 120 dB

▪ Human hearing depends on both the frequency and the intensity.

Vibration & Resonance

▪ Forced vibrations: The tendency of one object to force another adjoining or interconnected object into vibrational motion

▪ Sympathetic vibrations: a vibration produced in one body by the vibrations of exactly the same period in a neighboring body

Forced Vibrations

▪ Sympathetic vibrations occur when a vibrating object forces another to vibrate as well.– A piano string vibrates the sound board.

– A guitar string vibrates the bridge.

▪ This makes the sound louder and the vibrations die out faster.– Energy is transferred from the string to the sound board or bridge.

Vibration & Resonance

▪ Natural frequency: The frequency or frequencies at which an object tends to vibrate with when hit, struck, plucked, strummed or somehow disturbed

▪ Resonance:when one object vibrating at the same natural frequency of a second object forces that second object into vibrational motion.

Resonance

▪ The red rubber band links the 4 pendulums.

▪ If a blue pendulum is set in motion, only the other blue pendulum will have large-amplitude vibrations.– The others will just move a small amount.

▪ Since the vibrating frequencies of the blue pendulums match, they are resonant.

Resonance

▪ Large amplitude vibrations produced when the frequency of the applied force matches the natural frequency of receiver– One blue pendulum was the driving force and the other was the receiver.

▪ Bridges have collapsed as a result of structural resonance.– Tacoma Narrows in the wind

– A freeway overpass during an earthquake

Click below to watch the Visual Concept.

Visual Concept

Resonance (Frequency)

Human Ear

▪ Transmits vibrations that cause nerve impulses

Pathway = Outer ear (ear canal)Eardrum3 bones (hammer, anvil, stirrup)CochleaBasilar membranes

Question 1

▪ When the decibel level of traffic in the street goes from 40 to 60 dB, how much louder does the traffic noise seem?

▪ How much greater is the intensity?

Question 2

▪ Of the following factors:– Intensity

– Speed of sound waves

– Frequency

– Decibel level

– Wavelength

– Amplitude

Which factors change the loudness of the sound?

Which factors change when pitch gets higher?

Question 3

▪ A tuning fork consists of two metal prongs that vibrate at a single frequency when struck lightly. What will happen if a vibrating tuning fork is placed near another tuning fork of the same frequency?