Part a: Finding the distance to the canyon wall

Given that sound travels at approximately 750 miles per hour, and it takes 4 seconds to hear the echo, the question asks for the distance to the canyon wall in feet.

Step 1: Convert the speed of sound to feet per second.

First, we need to convert the speed of sound from miles per hour to feet per second:

$1 \text{ mile} = 5280 \text{ feet}$ $750 \text{ miles per hour} = 750 \times 5280 = 3,960,000 \text{ feet per hour}$ Since there are 3600 seconds in an hour, the speed of sound in feet per second is:

$\frac{3,960,000}{3600} = 1,100 \text{ feet per second}$

Step 2: Calculate the total distance traveled by sound.

In 4 seconds, the total distance the sound travels (there and back) is:

$\text{Distance traveled} = 1,100 \text{ feet/second} \times 4 \text{ seconds} = 4,400 \text{ feet}$

Step 3: Calculate the distance to the canyon wall.

Since the sound travels to the canyon wall and back (i.e., the total distance is twice the distance to the wall), the distance to the canyon wall is:

$\text{Distance to the canyon wall} = \frac{4,400}{2} = 2,200 \text{ feet}$

So, the canyon wall is 2,200 feet away.

Part b: Finding the time for the echo

Now, you are 1,925 feet away from the canyon wall, and we need to determine how long it takes to hear the echo.

Step 1: Calculate the total distance traveled by sound.

The sound travels to the wall and back, so the total distance the sound travels is:

$\text{Total distance} = 2 \times 1,925 = 3,850 \text{ feet}$

Step 2: Calculate the time taken.

Since sound travels at 1,100 feet per second, the time it takes to travel 3,850 feet is:

$\text{Time} = \frac{3,850 \text{ feet}}{1,100 \text{ feet/second}} \approx 3.5 \text{ seconds}$

So, it will take approximately 3.5 seconds to hear the echo.

Final Answers:

• a) The canyon wall is 2,200 feet away.
• b) It will take about 3.5 seconds to hear the echo.

Do you need further details or have any questions?

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Here are some related questions to explore:

1. How does temperature affect the speed of sound?
2. What if the sound took 6 seconds to return—how far would the canyon wall be?
3. How would the echo time change if the canyon wall was 3,000 feet away?
4. What is the relationship between distance and time for sound waves?
5. How fast does sound travel in water compared to air?

Tip: The speed of sound varies with altitude and air temperature.