Here’s an interesting math puzzle. If you’re at a concert that’s also being broadcast live on the radio, who will hear the music first? Will it be you, or people listening on the radio?  In this video, I’ll show you how to use the speed of sound versus the speed of light to find the answer. Watch to learn how it works…and who will hear the music first!


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Download Student Worksheet & Exercises


So based on the conditions given in the video, the person listening on the radio will actually hear the music just slightly before you do! How strange is that?!?


Exercises


  1. At what speed do electromagnetic waves travel?
  2. What is the speed of sound though the air?
  3. What is the relation between time, distance and speed?
  4. A particle travels at a speed of 10 meters per second in the air for 20 seconds. Determine the distance that it covers.
  5. Convert the answer from question #1 above to the units of minutes instead of seconds.
  6. Convert the answer from question #2 above to the units of minutes instead of seconds.
  7. A radio listener hears the news from her radio 12,000 miles away from the broadcasting center. Determine the time it takes to receive the sound.(Use the speed from #1 above)
  8. A person attends a public rally at stand at 200 feet away from the stage so that they can hear the person’s real voice without the use of speakers. Determine the time taken to hear the sound. (Use the speed from #2 above.)
  9. In a phone conversation, it takes 1 second for a person to hear her friend from the other end. How far are these people from one another?
  10. During a public lecture, a student at the back takes 0.1 seconds to hear what the lecturer is saying. What is the distance between the lecturer and the student?

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Comments

2 Responses to “Math at a Rock Concert”

  1. Yes, you are correct that there are several additional factors to include when doing this problem completely. However, since the distance between their mouth and the microphone is short compared with the other distances in the problem, we neglected it (which is a common practice in engineering problems). Also, this problem was intended to illustrate the difference in speed between sound waves and radio waves, so we also ignored the processing time of the electronics equipment. I like how you picked up on the additional terms you’d be asked to calculate in a college level course! 🙂

    And no, volume doesn’t affect sound speed below Mach 1, and doesn’t affect radio wave speed either. Great questions!

  2. Emily Brock says:

    What about the time it takes for the sound to get to the microphone that is recording them, the time it takes for the device to process the sound and send out the radio waves, and the time it takes for the radio on the other end to process it, and the time it takes for the sound to get from the radio to the other person?
    If the microphone were 30 feet from the band, and the other person was 70 feet away from the radio, then the person at the concert would hear the sound at least 1/186 second quicker.
    David

    Does volume affect how quickly the person at the concert hears it?
    David’s mom (Emily)