Question

Sound Travels about 750 miles per hour.

A) Suppose it takes about 1.5 seconds to hear the echo. How far away is the canyon wall, in feet?
For this I got 825 ft

B) Suppose you stand 1,925 feet from the canyon wall and sound the horn. How long will it take to hear the echo? (I'm stuck on this)

Answer 1

1. 1,650 ft

2. 1.75 sec

Explanation:

Sound travels about 750 miles per hour. Convert the sound's speed into feet per second. Since

1 mile = 5,280 feet, then

750 miles = 750·5,280 feet = 3,960,000 feet.

1 hour = 60 minutes,

1 minute = 60 seconds, then

1 hour = 3,600 seconds.

Hence,

`750\ (mi)/(h)=(3,960,000)/(3,600)\ (ft)/(sec)=1,100\ (ft)/(sec).`

1. If it takes about 1.5 seconds to hear the echo, then the canyon is

`1100\cdot 1.5=1,650\ ft` away.

2. If you stand 1,925 feet from the canyon wall and sound the horn, then it will take

`(1,925)/(1,100)=1.75\ sec`

to hear the echo.

Answer 2

A. 824 feet B. 3.5 seconds

Explanation:

A) We hear the echo after 1.5 seconds. Let the distance from a person to canyon wall is x miles.

Then echo of a sound will travel the distance (2x) miles

Since speed =
`(Distance)/(Time)`

Here speed of sound = 750 miles per hour

or =
`(750)/(60* 60)` miles per second

= 0.208 miles per second

and time = 1.5 seconds

Now we plug in the values in the formula

0.208 =
`(2x)/(1.5)`

x =
`(1.5* 0.208)/(2)`

= 0.156 miles ≈ 0.156 × 5280

≈ 824 feet.

B) If the person is standing 1,925 feet from the canyon wall then we have to find the time after which he will hear the echo.

Since speed =
`(Distance)/(time)`

Here speed = 750 miles per hour

and Distance = 2 × 1925 feet or
`(2* 1925)/(5280)` = 0.73 miles

We will plug in these values in the formula.

750 =
`(0.73)/(t)`

t =
`(0.73)/(750)`

= 0.00097 hours

≈ 0.00097 × 3600 seconds

≈ 3.5 seconds