Question

5. How long would it take sound waves traveling through air that is 68°F to travel 2,058 meters? Use an equation to solve the problem.

Answer 1

Answer:

6 seconds

Step-by-step explanation:

Temperature of air = $68^{\circ}\text{F}$

Converting to Celsius

$T=(68-32)\dfrac{5}{9}=20^{\circ}\text{C}$

Speed of sound in air is given by

$v=331.3\sqrt{1+\dfrac{T}{273.15}}\\\Rightarrow v=331.3\sqrt{1+\dfrac{20}{273.15}}\\\Rightarrow v=343.21\ \text{m/s}$

d = Distance to travel = 2058 m

Time is given by

$t=\dfrac{d}{v}\\\Rightarrow t=\dfrac{2058}{343.21}\\\Rightarrow T=5.99\approx 6\ \text{s}$

Time taken to travel 2058 m is 6 seconds.