Sound Basics By Stephen Richardson

Mechanical Waves A wave is a disturbance of a medium which transports energy through the medium without permanently transporting matter. In a wave, particles of the medium are temporarily displaced and then return to their original position. In a transverse wave, particles of the medium are displaced in a direction perpendicular to the direction of energy transport. In a longitudinal wave, particles of the medium are displaced in a direction parallel to energy transport. http://www.physicsclassroom.com/mmedia/waves/lw.cfm

Mechanical Waves (From D. Russell's website at Kettering University, Flint, MI)

Sound-A longitudinal Wave

Water-A Transverse Wave

Modeling Waves

Wave Formulas 𝑻= 𝟏 𝒇 𝑝𝑒𝑟𝑖𝑜𝑑= 1 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝒇= 𝟏 𝑻 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦= 1 𝑝𝑒𝑟𝑖𝑜𝑑 𝒗=𝝀𝒇 𝑠𝑝𝑒𝑒𝑑=𝑤𝑎𝑣𝑒𝑙𝑒𝑛𝑔𝑡ℎ·𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦

Wave Interference Waves can interfere with each other causing constructive and destructive interference.

Beat Frequency If two sounds are propagating at the same time and have different frequencies, then there is an obvious difference in frequency. The two different frequencies cause both constructive and destructive interference in the waves that is heard as a “wa-wa-wa” sound which results from repeated cycles of constructive interference, followed by destructive interference between the two waves. The interfering sounds will have a regularly spaced increase and decrease of sound which is called beats. The beat caused by the interfering waves has frequency. 𝒇 𝒃 = 𝒇 𝟐 − 𝒇 𝟏

Sound - A Form of Energy All waves transport energy. The intensity of a sound wave is a measure of the energy the sound wave is caring. The intensity is defined as the power (in watts) trans- mitted by a wave to the unit area (in square meters) that is perpendicular to the waves. 𝑰= 𝑷 𝑨 𝐼𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦= 𝑃𝑜𝑤𝑒𝑟 𝐴𝑟𝑒𝑎 Sound intensity is difficult to measure directly since you have to choose some portion of a wave front and then know how much power is distributed over the area of that portion. There are handheld devices for measuring the intensity of sound.

Sound Intensity (𝑰) Example: Suppose two square meters of a sound wave front has 2.0 × 10-5 watts of power distributed over its area. Compute the intensity of the sound. Example: A portion of a wave front has 25 W of power distributed over an area of 0.25 square meters. Compute the Intensity of the sound. Is the sound wave dangerous? Example: Suppose the energy of a sound wave is distributed over an area so that it has a power rating of 35 W. Compute the area. Assume the intensity of the sound is 1.0 × 10-4 W/m2.

Sound Intensity Level (dB) Source Intensity Intensity 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

Sound Pressure Level(dB)

Sound Intensity Level (SIL) 𝑆𝐼𝐿(𝑑𝐵)=10𝑙𝑜𝑔 𝐼 𝐼 0 𝑑𝐵 𝐼=𝑖𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑜𝑢𝑛𝑑 𝐼 0 =𝑖𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑 𝑜𝑓 ℎ𝑒𝑎𝑟𝑖𝑛𝑔 𝐼 0 =1.0× 10 −12 𝑊 𝑚 2

Doppler Effect(Sound) When the source of a sound is moving the perceived frequency of the sound is different than the actual frequency generated by the source. The wavelength of a sound wave is stretched or compressed by the motion. Since the wavelength changes, then the frequency must change. In fact, when the source of a sound is moving the speed, wavelength, and frequency of the original sound wave are all affected. The perceived change is frequency is called the Doppler Effect.

Doppler Effect

Practice Problems Two sound waves have frequency 880 Hz and 780 Hz respectively. If the air temperature is 30.0˚C, then… a. Compute the velocity of each sound wave in meters per second. (Note: This is one calculation. b. Compute the wavelength of each sound in cm. c. The first sound wave has frequency 880Hz. If a second sound is generated with a frequency of 885 Hz, then what is the beat frequency between the two sounds? 2) A vibration completes 14.0 cycles in 0.50 seconds. Compute the frequency and period of the vibration. Express your answer for period in scientific notation. Hint: Frequency is measured in cycles per second.

Practice Problems 3) Use the formula 𝑆𝐼𝐿 𝑑𝐵 =10𝑙𝑜𝑔 𝐼 𝐼 0 dB to compute the sound intensity level (SIL) of a sound that has an intensity of 3.0× 10 −3 𝑊 𝑚 2 . Remember that 𝐼 0 =1.0× 10 −12 𝑊 𝑚 2 . 4) A loud speaker produces a sound with 10.0 watts of power per 55.0 square meters. a. Compute the intensity of the sound. b. Compute the sound intensity level that is produced by the loud speaker. Is the sound level comfortable? A commercial aircraft has a SPL of 120 dB at about 500 feet away from the engine.

Wave Amplitude A wave’s greatest displacement from equilibrium is called its amplitude (a).