A fan at a rock concert is 50.0 m from the stage, and at this point the sound in
ID: 1700325 • Letter: A
Question
A fan at a rock concert is 50.0 m from the stage, and at this point the sound intensity level is 114 dB. Sound is detected when a sound wave causes the tympanic membrane (the eardrum) to vibrate . Typically, the diameter of this membrane is about 8.40 mm in humans
A.How much energy is transferred to her eardrums each second ? (in J)
D.Compare the mosquito's speeds found in parts (B) and (C).
A fan at a rock concert is 50.0 m from the stage, and at this point the sound intensity level is 114 dB. Sound is detected when a sound wave causes the tympanic membrane (the eardrum) to vibrate . Typically, the diameter of this membrane is about 8.40 mm in humans A.How much energy is transferred to her eardrums each second ? (in muJ) B.How fast would a 2.00 {mg} mosquito have to fly to have this much kinetic energy?(in m/s) C.How fast a typical 2.0 {mg} mosquito would have to fly (in {mm}/{s}) to have an amount of energy delivered to the eardrum each second when someone whispers (20 {dB}) a secret in your ear?(in mm/s) D.Compare the mosquito's speeds found in parts (B) and (C).Explanation / Answer
distance r = 50 m sound intensity L = 114 dB diameter d = 8.4 mm = 8.4 * 10 ^-3 m Radius R = d / 2 = 4.2 * 10 ^ -3 m area a = Pi * R ^ 2 = 55.41 * 10^-6 m^ 2 we know L = 10 log ( I / Io) from this intensity I = Io * 10^ (L/10) = 10^-12 W/m^ 2 * 10^(114/10) = 0.2511 W / m^ 2 energy is transferred to her eardrums each second E = I * A (b). mass m = 2.00* 10 ^ -3 g = 2* 10 ^ -6 kg kinetic energy K = E ( calculated above ) we know K = ( 1/ 2) mv^ 2 from this required speed v = sqrt [ 2K / m] C. mass m = 2* 10^ -6 kg intensity level L ' = 20 dB intensity I' = Io * 10^ (L '/10) = 10^-12 W/m^ 2 * 10^(20/10) = 10 ^ -10 W / m^ 2 from this enenrgy E ' = I ' * A So, required speed v ' = sqrt [ 2E ' m/] (d). required ratio = v / v '
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