Chapter 5: Problem 48

What is the minimum distance between the reflector and the listener to hear the echo, when the speed of sound in air is \(330 \mathrm{~m} \mathrm{~s}^{-1}\) ?

Short Answer

Expert verified

Answer: The minimum distance between the reflector and the listener for the listener to hear an echo is 16.5 meters.

Step by step solution

Determine the time for a listener to hear an echo

According to the physics of sound waves, a listener can hear an echo if the sound wave has to travel for at least \(0.1 \mathrm{~s}\) to and from the reflector. So, the total time the sound wave needs to travel from the listener to the reflector and back to the listener is at least \(0.1 \mathrm{~s}\).

Calculate the total distance traveled by the sound wave

Using the formula for distance, \(distance = speed \times time\), we can calculate the total distance traveled by the sound wave. In this case, the speed of sound in air is \(330 \mathrm{~m} \mathrm{~s}^{-1}\) and the total time is \(0.1 \mathrm{~s}\). The formula becomes: \(distance_{total} = 330 \mathrm{~m} \mathrm{~s}^{-1} \times 0.1\mathrm{~s} = 33 \mathrm{~m}\)

Find the minimum distance between the reflector and the listener

The sound wave must travel to the reflector and back to the listener, so the distance between the reflector and the listener is half of the total distance traveled by the sound wave. To find the minimum distance, we simply divide the total distance by 2: \(distance_{min} = \frac{33 \mathrm{~m}}{2} = 16.5 \mathrm{~m}\) So the minimum distance between the reflector and the listener for the listener to hear an echo is \(16.5 \mathrm{~m}\).

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What is the minimum distance between the reflector and the listener to hear the echo, when the speed of sound in air is \(330 \mathrm{~m} \mathrm{~s}^{-1}\) ?

Short Answer

Step by step solution

Determine the time for a listener to hear an echo

Calculate the total distance traveled by the sound wave

Find the minimum distance between the reflector and the listener

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