You can buy a measuring device billed as a "sonic tape measure." Describe how a device equipped with an (ultrasonic) speaker, a microphone, and a precision timer could be used to measure the distance from the device to a wall (for example).

Short Answer

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Question: Explain how a sonic tape measure can be used to measure the distance from the device to a wall using an ultrasonic speaker, a microphone, and a precision timer. Answer: A sonic tape measure measures distance by emitting a high-frequency sound wave from its ultrasonic speaker, which travels towards a wall and bounces back as an echo. The device's microphone detects the echo, and its precision timer measures the time taken for the round trip. The distance to the wall is calculated using the formula: Distance = (Speed of sound * Time taken) / 2, accounting for the fact that the sound wave travels the distance twice (to the wall and back). The speed of sound in air (approx. 343 meters per second) is constant, allowing for accurate distance calculations.

Step by step solution

01

Understanding the sonic tape measure principle

A sonic tape measure works by emitting a sound wave using the ultrasonic speaker and then detecting the echo of this wave when it bounces back off a wall or object using the microphone. It then calculates the distance based on the time it took for the sound wave to travel to the object and back.
02

Emit the sound wave

When the sonic tape measure is aimed at a wall, and the device is activated, the ultrasonic speaker will emit a high-frequency sound wave. This sound wave will travel through the air towards the wall. The frequency of this sound wave is typically beyond the range of human hearing (above 20,000 Hz).
03

Receive the reflected sound wave

Once the sound wave hits the wall, it will be reflected back towards the device. The microphone present in the device will then pick up this reflected sound wave (echo) and convert it back into an electrical signal.
04

Measure the time taken for the round trip

The precision timer in the sonic tape measure starts counting as soon as the sound wave is emitted and stops when the echo is received. Since the speed of sound is constant in a given medium (in this case, air), we can use the elapsed time to determine the distance traveled by the sound wave.
05

Calculate the distance

To calculate the distance to the wall, we use the following formula: Distance = (Speed of sound * Time taken) / 2 Here, we divide by 2 because the sound wave travels to the wall and back, covering the distance twice. In air, the speed of sound is approximately 343 meters per second or 1,125 feet per second. Once we have the time taken for the round trip, we can calculate the distance to the wall using this formula. This is how a sonic tape measure equipped with an ultrasonic speaker, a microphone, and a precision timer can be used to measure the distance from the device to a wall.

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