Speed of sound: A pipe that is 20.0 m long and 10.0 cm in diameter contains olive oil. The density of the olive oil is 890 kg/m³ and the bulk modulus is 1.3 × 10⁹Pa. A 3.4-Hz longitudinal wave is transmitted in the oil. How many milliseconds does it take for the wave to travel the length of the pipe in the oil? A) 17 ms B) 15 ms C) 14 ms D) 13 ms E) 12 ms

Question

Quizplus · Accepted Answer

The speed of sound in a fluid is given by:$$v = \sqrt{\frac{B}{ho}}$$where:* v is the speed of sound (m/s)* B is the bulk modulus (Pa)* ρ is the density (kg/m^3)In this problem, we are given the following information:* B = 1.3 × 10^9 Pa* ρ = 890 kg/m^3* L = 20.0 m* f = 3.4 HzWe can use the formula above to calculate the speed of sound in the olive oil:$$v = \sqrt{\frac{B}{ho}} = \sqrt{\frac{1.3 	imes 10^9 	ext{ Pa}}{890 	ext{ kg/m}^3}} = 143.4 	ext{ m/s}$$The time it takes for the wave to travel the length of the pipe is:$$t = \frac{L}{v} = \frac{20.0 	ext{ m}}{143.4 	ext{ m/s}} = 0.139 	ext{ s} = 139 	ext{ ms}$$Therefore, the correct answer is A) 17 ms.

Speed of Sound: a Pipe That Is 20