Question

A person with his ear to the ground, sees a huge stone strikethe concrete pavement. A moment later two sounds are heard from theimpact: one travels n the air and the other in the concrete, andthey are 2.2 s apart. How far away did the impact occur?
*The speed of sound for air is 343 m/s, for concrete˜3000.
Please show how you set up the problem and how you got youranswer.

Answer 1

Answer:

852.014 m

Explanation:

The speed of sound in air = 343 m/s = $v_a$

The speed of sound in concrete = 3000 m/s = $v_c$

The distance the sound traveled = s

Time between the sounds heard  = 2.2 seconds

Time = Distance / Speed

Time taken by sound travel through air

$\frac{s}{v_a}=\frac{s}{343}$

Time taken by sound travel through concrete

$\frac{s}{v_c}=\frac{s}{3000}$

So,

$\frac{s}{343}-\frac{s}{3000}=2.2\\\Rightarrow \frac{3000s-343s}{1029000}=2.2\\\Rightarrow \frac{2657s}{1029000}=2.2\\\Rightarrow s=\frac{1029000\times 2.2}{2657}\\\Rightarrow s=852.014\ m$

The impact occurs 852.014 m away from the person.