# Train Whistle Echo: Calculating Distance & Temperature Effects

• Xoloti
In summary, a stationary railroad whistle is sounded and an echo is heard 4.0 seconds later by a train's engineer. Using the equation d=rt, we can determine that the reflecting surface is 686 meters away. If the temperature of the air increases, the speed of sound also increases, resulting in a shorter distance of 686 meters.

## Homework Statement

a)a stationary railroad whistle is sounded. An echo is heard 4.0 seconds later by a train's engineer. If the speed of sound is 343 m/s, how far away is the reflecting surface?
b) If the temperature of the air increased, how would this change your answer?

d=rt
x=xt/2

## The Attempt at a Solution

I got part a right. x=(343*4)/2 =686 because the sound has to travel twice
I do not know part b

Xoloti said:

## Homework Statement

a)a stationary railroad whistle is sounded. An echo is heard 4.0 seconds later by a train's engineer. If the speed of sound is 343 m/s, how far away is the reflecting surface?
b) If the temperature of the air increased, how would this change your answer?

d=rt
x=xt/2

## The Attempt at a Solution

I got part a right. x=(343*4)/2 =686 because the sound has to travel twice
I do not know part b
Welcome to the PF.

How does the speed of sound in air change with a change in air temperature?

berkeman said:
Welcome to the PF.

How does the speed of sound in air change with a change in air temperature?
Higher the temperature faster the speed of sound. Thanks!

Xoloti said:
Higher the temperature faster the speed of sound. Thanks!
Really? That may be true, but it's counter-intuitive for me. Do you have a link to a reference that says that?

## 1. How does a train whistle echo help in calculating distance?

A train whistle echo can help in calculating distance by measuring the time it takes for the sound to reach a listener and then return as an echo. This time is then used in the distance formula (distance = speed x time) to calculate the distance between the train and the listener.

## 2. Why is temperature important in the calculation of train whistle echo?

Temperature is important in the calculation of train whistle echo because it affects the speed of sound. Sound travels faster in warmer temperatures and slower in colder temperatures. Therefore, the temperature must be taken into account in order to accurately calculate the distance based on the time it takes for the sound to travel.

## 3. How does the speed of sound change with temperature?

The speed of sound increases as the temperature increases. This is because the molecules in warmer air have more energy and can vibrate faster, allowing sound to travel faster. On the other hand, colder temperatures result in slower vibrating molecules, thus decreasing the speed of sound.

## 4. Can other factors affect the accuracy of train whistle echo calculations?

Yes, other factors such as wind, humidity, and elevation can also affect the speed of sound and therefore impact the accuracy of train whistle echo calculations. These factors can alter the temperature and air density, which in turn affects the speed of sound.

## 5. How can train whistle echo calculations be used in real-life scenarios?

Train whistle echo calculations can be used in various real-life scenarios, such as determining the distance of a train from a crossing or a station, calculating the speed of a train based on the time it takes for the whistle to travel, and even in meteorology to measure temperature and wind speed.