Question

A hiker determines the length of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 3.7s\; s after shouting. The speed of sound in air is 343 m/s\rm m/s. Determine the length of the lake. Express your answer to two significant figures and include the appropriate units.

Answer 1

To solve the exercise it is necessary to take into account the definition of speed as a function of distance and time, and the speed of air in the sound, as well

$v=\frac{d}{t}$

Where,

V= Velocity

d= distance

t = time

Re-arrange the equation to find the distance we have,

d=vt

Replacing with our values

$d= (343)(3.7)$

$d= 1269.1m$

It is understood that the sound comes and goes across the entire lake therefore, the length of the lake is half the distance found, that is

$L_{lake} = \frac{d}{2}$

$L_{lake} = \frac{1269.1}{2}$

$L_{lake} = 634.55m$

Therefore the length of the lake is 634,55m