## Find the speed of sound yourself!

An experiment from *The Jinson Twins, Science Detectives, and the Mystery of Echo Lake.*

In the Mystery of Echo Lake, Joe and Debbie Jinson, with Mr. Benjamin’s help, find a treasure sunk in the middle of Echo Lake. They use clues written in a poem on a treasure map to figure out where to search for the treasure. The clues specify two measurements that reveal where the treasure is located.

One measurement is a direction from a prominent landmark, The Owl’s Eye, a rock formation on a hill on one side of Echo Lake. The treasure is sunk somewhere along a line that runs due West to the Owl’s Eye, but the twins don’t know where along that line the treasure lies. They need another measurement to tell them where along the line the treasure is. The other measurement isn’t another compass direction, or a distance measured in a usual way. Instead, the other measurement is the length of time it takes sound to travel out from the boat that the twins, Mr. Benjamin, and Mrs. Gray are in, and echo back to the boat. When that time is exactly right, and the Owl’s Eye lies due West, then the boat is right above the treasure.

The twins know the echo is right when two repeated words of an old sea shanty exactly coincide. That happens when the twins sing the song at a particular tempo. By singing the song at the right tempo and listening for the echo, the twins use the speed of sound to measure the distance to the place that is producing the echo.

Since the measurement of the distance depends on the speed of sound, and since the speed of sound changes depending on the temperature, the twins need to sing the song at the right temperature for the measurement to be right. The treasure map tells the twins the right temperature, but not directly. Instead, it leaves a clue to the right temperature by telling the twins that they have to sing the song when the crickets that live near the lake chirp at a particular rate. The rate the crickets chirp depends on the temperature, so by telling the twins to sing the song and look for the treasure when the crickets chirp at a certain rate, the map tells the twins what temperature it needs to be for the twins to sing the song and find the treasure.

At one point in the book, Mr. Benjamin shows the twins a formula that describes, approximately, how fast sound travels and how the speed of sound depends on the temperature. Here is the formula:

Vs = 331.4+0.6Tc m/sec

where Vs = speed of sound, and

Tc = temperature in degrees Celsius

Mr. Benjamin found the formula in a few minutes of searching on the World Wide Web. But, is this right? Can you trust this formula? (And can you trust everything you find on the Web?) Well, you don’t have to trust the formula. You can determine the speed of sound yourself! You can see if Mr. Benjamin was right, and you don’t need much elaborate equipment either. The following experiment uses an echo to help you determine the speed of sound. And, if you want, you can determine the speed of sound at several different temperatures to see whether the speed of sound really does depend on the temperature. Here’s how:

Materials

1. A watch that can measure seconds.

2. A tape measure.

3. A solid wall, outdoors, away from other walls, so that the wall can make a clear, sharp echo.

4. Your hands, to clap. (Optional equipment: a small drum that can make a short, sharp sound).

5. A helper.

6. Optional equipment: A thermometer.

Procedure

1. Go to the wall.

2. Stand about 20-30 meters away from the wall.

3. Clap your hands (or bang the drum).

4. Listen for the echo. If you don’t hear a good echo, then find a place where you do hear a good echo.

5. When you hear a good echo, start clapping (or drumming) evenly. Increase or decrease your clapping (or drumming) rate until you hear the sound from the clap (or drumbeat) you make exactly coincide with the echo of the clap (or drumbeat) you made just before.

6. Keep clapping (or drumming) steadily at that rate and have your assistant count how many claps (or drumbeats) you make in 10 seconds, measured by the watch.

7. Divide the number of claps (or drumbeats) by 10 to give you the number of claps (or drumbeats) you are making per second. This is the time (call it ‘t’) it took for the sound to travel from your hands to the wall and back.

8. Use the tape measure to measure the distance between you and the wall making the echo.

9. Double the distance you measure to the wall to find out how far the sound traveled (call it ‘d’).

10. Divide the distance the sound traveled by the time it took to make the trip. This is the speed of sound (call it ‘s’) under the conditions you used to make the measurement. So, s=d/t. You can measure the temperature, if you want.

11. Compare your measurement to the formula. Is it close? (If you don’t have a thermometer, you can estimate the temperature or use the temperature from a public thermometer (like on a sign, TV or radio, or the Web.)

You can also measure the speed of sound at several different temperatures and see how the speed of sound changes depending on the temperature. If you do make measurements at several different temperatures, you can then see whether the speed of sound does depend on the temperature. It may also help to graph out the results yourself.

Finally, what’s the use of knowing the speed of sound? Well, one use you might find interesting is figuring out how far away lightning is. Light travels so fast that over distances we commonly experience in daily life we can usually think of it as traveling instantaneously, but sound travels much more slowly. So, the next time you are in a thunderstorm, measure the time between the lightning flash and the thunder, and multiply that time by the speed of sound. That will tell you how far away the lightning was.

One measurement is a direction from a prominent landmark, The Owl’s Eye, a rock formation on a hill on one side of Echo Lake. The treasure is sunk somewhere along a line that runs due West to the Owl’s Eye, but the twins don’t know where along that line the treasure lies. They need another measurement to tell them where along the line the treasure is. The other measurement isn’t another compass direction, or a distance measured in a usual way. Instead, the other measurement is the length of time it takes sound to travel out from the boat that the twins, Mr. Benjamin, and Mrs. Gray are in, and echo back to the boat. When that time is exactly right, and the Owl’s Eye lies due West, then the boat is right above the treasure.

The twins know the echo is right when two repeated words of an old sea shanty exactly coincide. That happens when the twins sing the song at a particular tempo. By singing the song at the right tempo and listening for the echo, the twins use the speed of sound to measure the distance to the place that is producing the echo.

Since the measurement of the distance depends on the speed of sound, and since the speed of sound changes depending on the temperature, the twins need to sing the song at the right temperature for the measurement to be right. The treasure map tells the twins the right temperature, but not directly. Instead, it leaves a clue to the right temperature by telling the twins that they have to sing the song when the crickets that live near the lake chirp at a particular rate. The rate the crickets chirp depends on the temperature, so by telling the twins to sing the song and look for the treasure when the crickets chirp at a certain rate, the map tells the twins what temperature it needs to be for the twins to sing the song and find the treasure.

At one point in the book, Mr. Benjamin shows the twins a formula that describes, approximately, how fast sound travels and how the speed of sound depends on the temperature. Here is the formula:

Vs = 331.4+0.6Tc m/sec

where Vs = speed of sound, and

Tc = temperature in degrees Celsius

Mr. Benjamin found the formula in a few minutes of searching on the World Wide Web. But, is this right? Can you trust this formula? (And can you trust everything you find on the Web?) Well, you don’t have to trust the formula. You can determine the speed of sound yourself! You can see if Mr. Benjamin was right, and you don’t need much elaborate equipment either. The following experiment uses an echo to help you determine the speed of sound. And, if you want, you can determine the speed of sound at several different temperatures to see whether the speed of sound really does depend on the temperature. Here’s how:

Materials

1. A watch that can measure seconds.

2. A tape measure.

3. A solid wall, outdoors, away from other walls, so that the wall can make a clear, sharp echo.

4. Your hands, to clap. (Optional equipment: a small drum that can make a short, sharp sound).

5. A helper.

6. Optional equipment: A thermometer.

Procedure

1. Go to the wall.

2. Stand about 20-30 meters away from the wall.

3. Clap your hands (or bang the drum).

4. Listen for the echo. If you don’t hear a good echo, then find a place where you do hear a good echo.

5. When you hear a good echo, start clapping (or drumming) evenly. Increase or decrease your clapping (or drumming) rate until you hear the sound from the clap (or drumbeat) you make exactly coincide with the echo of the clap (or drumbeat) you made just before.

6. Keep clapping (or drumming) steadily at that rate and have your assistant count how many claps (or drumbeats) you make in 10 seconds, measured by the watch.

7. Divide the number of claps (or drumbeats) by 10 to give you the number of claps (or drumbeats) you are making per second. This is the time (call it ‘t’) it took for the sound to travel from your hands to the wall and back.

8. Use the tape measure to measure the distance between you and the wall making the echo.

9. Double the distance you measure to the wall to find out how far the sound traveled (call it ‘d’).

10. Divide the distance the sound traveled by the time it took to make the trip. This is the speed of sound (call it ‘s’) under the conditions you used to make the measurement. So, s=d/t. You can measure the temperature, if you want.

11. Compare your measurement to the formula. Is it close? (If you don’t have a thermometer, you can estimate the temperature or use the temperature from a public thermometer (like on a sign, TV or radio, or the Web.)

You can also measure the speed of sound at several different temperatures and see how the speed of sound changes depending on the temperature. If you do make measurements at several different temperatures, you can then see whether the speed of sound does depend on the temperature. It may also help to graph out the results yourself.

Finally, what’s the use of knowing the speed of sound? Well, one use you might find interesting is figuring out how far away lightning is. Light travels so fast that over distances we commonly experience in daily life we can usually think of it as traveling instantaneously, but sound travels much more slowly. So, the next time you are in a thunderstorm, measure the time between the lightning flash and the thunder, and multiply that time by the speed of sound. That will tell you how far away the lightning was.