Q26. - Algebra 2

Question

When a sound travels through water, the distance $y$ in meters that the sound travels in $x$ seconds is given by the equation $y=1440x$.

 

In air, the equation is $y=343x$. Does sound travel faster in air or water? Explain.

Step-by-Step Solution

Answer

The sound travels faster in the water.

Step 1 – Given information.

The distance y in meters that the sound travels through water in x seconds is:

$y=1440x$

The distance y in meters that the sound travels through air in x seconds is:

$y=343x$

Step 2 – Find the speed of sound in water.

Substitute x=1 in $y=1440x$.

$\begin{array}{c}y=1440\left(1\right)\\ =1440\end{array}$

So, the sound travels 1440 meter per second.

Step 3 – Find the speed of sound in air and then compare both speeds.

Substitute x=1 in $y=343x$.

$\begin{array}{c}y=343\left(1\right)\\ =343\end{array}$

So, the sound travels 343 meter per second.

Since $1440>343$, therefore the speed of sound is greater in the water.

 

Thus, the sound travels faster in the water.