problem15_78

University Physics with Modern Physics with Mastering Physics (11th Edition)

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15.78: a) Consider the derivation of the speed of a longitudinal wave in Section 16.2. Instead of the bulk modulus B , the quantity of interest is the change in force per fractional length change. The force constant k is the change in force force per length change, so the force change per fractional length change is , L k the applied force at one end is ) )( ( v v L k F y = and the longitudinal impulse when this force is applied for a time t is . v v Lt k y The change in longitudinal momentum is
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Unformatted text preview: y v L m vt ) ) (( and equating the expressions, canceling a factor of t and solving for . gives 2 2 m k L v v ′ = An equivalent method is to use the result of Problem 11.82(a), which relates the force constant k ′ and the “Young’s modulus” of the Slinky . or , , A L k Y L YA k TM ′ = = ′ The mass density is (16.8) Eq. and ), ( AL m ρ = gives the result immediately. b) s. m 90 . 4 ) kg 250 . ( ) m N 50 . 1 ( ) m 00 . 2 ( =...
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