Questions: Here is a procedure used in a middle school science class to find the speed of sound in air. A student takes two erasers and begins to bang then together with a regular beat perhaps at a rate of 20 'claps' in 10 second - in front of the brick wall of the school building. The student begins walking backward until she can't hear the echo of the erasers anymore. Explain, in terms of the principles of waves explored in this Lesson, how this procedure is able to estimate the speed of sound in air.

Solution Steps

When the student bangs the erasers together, sound waves are produced. These sound waves travel through the air, hit the brick wall, and reflect back as an echo. The time it takes for the sound to travel to the wall and back is related to the speed of sound in air.

The student walks backward until she can no longer hear the echo. This distance is crucial because it represents the point where the time interval between the original sound and the echo is too short for the human ear to distinguish. This distance can be used to estimate the speed of sound.

The student claps the erasers at a regular rate of 20 claps in 10 seconds, which means each clap occurs every 0.5 seconds. This regular interval helps in determining the time it takes for the sound to travel to the wall and back.

The speed of sound \( v \) can be calculated using the formula: \[ v = \frac{2d}{t} \] where \( d \) is the distance to the wall and \( t \) is the time interval for the sound to travel to the wall and back. Since the student can no longer hear the echo, the time interval \( t \) is approximately equal to the time between claps, which is 0.5 seconds.

Final Answer