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M is for Music



To investigate how echoes are formed and how they can be used to calculate distance.

Review with students what they learned in M is for Musicabout how sound travels. (Sound moves as waves. It travels away from a vibrating object in every direction.)


Physical Science, Grades 58, Transfer of Energy: Energy is a property of many substances and is associated with...sound....


30 minutes


  • paper

  • pencils

  • calculators


Have students research the construction of amphitheaters, both ancient and modern. What materials are used to improve the sound quality? What structural issues are considered? Where is the audience placed in relation to the orchestra? Do all seats experience the same sound?

  • Ask if anyone knows what the speed of sound is. (It varies with temperature, pressure, and medium, but for this activity, well say it moves through air at 335 m/sec.) Write 335 m/secon the board. Explain that this is the approximate speed at which sound travels through air.

  • Now explain that while sound waves pass through air, they bounce off solid surfaces. Some of this bounced sound is reflected back toward the source.

  • Knowing these facts, challenge students to explain why it is that a hiker in the mountains will hear several echoes of a word she utters a single time. (The sound waves bounce off several mountains at different distances from the yeller, and so return to the yeller at different times. In limited cases, the sound may also be bouncing from one mountain to another before returning to the yeller.)

  • Explain to students that they can use echo time to calculate how far away a mountain is from a hiker. Pose the following problem: A hiker yells the word hifrom a mountain on one side of a valley across to a mountain on the other side. She hears the word echoed back 1.2 seconds later. How far away is the mountain on the other side of the valley? (Remind students that distance rate time. You may want to write this equation on the board.)

  • Help students as needed to solve the problem: 335 m/sec 1.2 sec 402 m 2 201 m (Note that in the final step the total distance must be divided by two since the sound travels back and forth in the 1.2 seconds.)

  • Create other math problems using the speed of sound, echo time, and distance between person and mountain. Or have pairs of students develop their own word problems and challenge their partners to solve them.

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