# Ps05soln - PHYSICS 218 SOLUTION TO HW 5 Created 1:24am Last updated October 1 2004 9:02pm 1(a A sound intensity at a level of I = 80 dB implies

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PHYSICS 218 SOLUTION TO HW 5 Created: September 28, 2004 1:24am Last updated: October 1, 2004 9:02pm 1. (a) A sound intensity at a level of I = 80 dB implies that 10 log 10 ( I/I 0 ) = 80, from this we get I/I 0 = 10 8 . From the data sheet on sound waves, I 0 = 10 - 12 W/m 2 . So we have an intensity I = 10 - 4 W/m 2 . The power P u passing through an area S = d 2 , where d = 30 m, is thus P u = I × d 2 = 9 × 10 - 2 W. And recall that power is the amount of energy transfered through the surface in unit time, the energy Δ E u that passes through the area in t = 1 s is Δ E u = 9 × 10 - 2 J. (b) Now assume that the singer radiates the sound uniformly in a quarter of the surface of the sphere, then at a radius of r = d , the total intensity is still given by I = 10 - 4 W/m 2 . However, the power P r produced is now given by P r = I × π r 2 = 2 . 8 × 10 - 1 W. The energy produced in t = 1 s is Δ E r = 2 . 8 × 10 - 1 J. (c) The total energy produced over a period of time t is given by E = P t . So the total sound energy E u and E r produced by the singer in one hour (3600 s) under the two assumptions made in part (a) and (b) at the fortissimo level are respectively E u = 324 J and E r = 1008 J. (The dynamics in music refers to the volume of the sound. The two basic dynamic indications in music are piano, meaning softly, usually abbreviated as p ; and forte, meaning loudly, usually abbreviated as f . The intermediate loudness or softness are mezzo-piano, mp , meaning half- quiet; and mezzo-forte, mf , meaning half-loud. Beyond f and p , there is also fortissimo, , meaning very loud; and pianissimo, pp , meaning very soft. And for lack of creativity, to indicate the more extreme loudness or softness, we just add more f ’s and p ’s. For instance, fortississimo ﬀf and pianississimo ppp are found in many compositions, and the dynamic level usually stops here. Anything more than that is very rare, partly because such word like

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## This note was uploaded on 09/28/2008 for the course PHYS 218 taught by Professor Pollack during the Fall '04 term at Cornell University (Engineering School).

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Ps05soln - PHYSICS 218 SOLUTION TO HW 5 Created 1:24am Last updated October 1 2004 9:02pm 1(a A sound intensity at a level of I = 80 dB implies

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