Unless indicated otherwise, assume the speed of sound in air to be v = 344 m/s. BIO Human Hearing. A fan at a rock concert is 30 m from the stage, and at this point the sound intensity level is 110 dB. (a) How much energy is transferred to her eardrums each second? (b) How fast would a 2.0-mg mosquito have to fly (in mm/s) to have this much kinetic energy? Compare the mosquito’s speed with that found for the whisper in part (a) of Exercise 16.13. 16.13 .. ?BIO Energy Delivered to the Ear. Sound is detected when a sound wave causes the tympanic membrane (the eardrum) to vibrate. Typically, the diameter of this membrane is about 8.4 mm in humans. (a) How much energy is delivered to the eardrum each second when someone whispers (20 dB) a secret in your ear? (b) To comprehend how sensitive the ear is to very small amounts of energy, calculate how fast a typical 2.0-mg mosquito would have to fly (in mm/s) to have this amount of kinetic energy.

Solution 16E Step 1 of 3: We know that I = 1 × 1010w m 2 2 The area of the tympanic membrane is A = r 3 r = 4.2 × 10 m and = 3.14 A = 3.14 × (4.2 × 10 ) = 55.39 × 10 m6 2 Step 2 of 3: a)Intensity is the energy per unit area per unit time E I = At We have to find energy so E = IAt =1 × 10 10 × 55.39 × 10 6× 1 =5.539 × 10 1J Step 3 of 3: b)The energy possessed by the object by virtue of its motion is called kinetic energy 1 2 K.E = m2 v = 2 K.E m = 2×5.5×1015 2×106 5 =7.4 × 10 m/s = 0.074 mm/s Step 1 of 3: We know that = 10 dB log( ) I0 The area of the eardrum is A = r 2 3 r = 4.2 × 10 m v = 0.074 mm A = 3.14 × 4.2 × 103 =55.39 × 10 m6 2 Step 2 of 3: a) = 110 dB I = 11 log (I0 I = 10 I = 0.1 w/m 2 0 Intensity is energy per unit area per unit time I = E At We have to find energy so E = IAt 6 =0.1 × 55.39 × 10 × 1 6 = 5.5 × 10 J