Two children setup a "telephone" by placing a long, slender aluminum (Y = 6.9 × 10¹⁰ N/m²) rod that has a length of 6.1-m between their two houses. To communicate, a child taps a coded message on one end. How long do the sound waves take to reach the other end? Note: the density of aluminum is 2700 kg/m³. A)1.2 × 10^-³ s B)2.4 × 10^-⁷ s C)8.0 × 10^-⁶ s D)6.3 × 10^-⁵ s E)1.1 × 10^-⁴ s

Question

Quizplus · Accepted Answer

The speed of sound in a solid is given by v = sqrt(Y/p), where Y is Young's modulus and p is the density. Plugging in the given values, we get v = sqrt(6.9 × 10^10 N/m^2 / 2700 kg/m^3) = 5100 m/s. The time it takes for the sound waves to reach the other end is then t = d/v = 6.1 m / 5100 m/s = 1.2 × 10^-3 s.

Two Children Setup a "Telephone" by Placing a Long, Slender