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The motion detector used in a physics lab sends and receives 30 kHz ultrasonic pulses. A pulse goes out, reflects off the object being measured, and returns to the detector. The lab temperature is 20 ∘C.

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Final answer:

The motion detector uses ultrasonic waves to measure distance by timing the round trip of a sound wave. Distance is calculated using the speed of sound and the time taken for the echo to return, and the calculation requires a division by 2 to account for the round trip. Calibration is important for accuracy as the speed of sound changes with temperature.

Step-by-step explanation:

The motion detector described is a classic example of how ultrasonic waves can be used to measure distance. A similar principle is applied in an automatic focus camera, which generates ultrasonic sound waves, captures their reflections off objects, and calculates the distance based on the time delay of the returning waves. The speed of sound in air at 20 ℃ is approximately 344 m/s. Therefore, if a sound wave returns after 0.150 seconds, we can calculate the distance to the object as follows:

Distance = Speed of Sound × Time / 2
Distance = 344 m/s × 0.150 s / 2
Distance = 25.8 meters
This calculation takes into account that the sound wave must travel to the object and back, making the total distance twice the distance we want to measure, hence the division by 2.

The ultrasonic range finder and technologies such as radar and Doppler shift applications in traffic law enforcement rely on similar concepts of wave reflection and frequency shifts to measure distance and speed.

To understand the effects of temperature on the calibration of such devices, the room temperature is required because the speed of sound in air changes with temperature, potentially influencing the accuracy of these measurements.

User Kirschstein
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Answer

Given,

Frequency of the ultrasonic pulse = 30 kHz

Speed of the sound = v = 343 m/s

wavelength of the wave emitted = ?

using formula


v = \\u \lambda


\lambda= (v)/(\\u)


\lambda= (343)/(30* 10^3)


\lambda=11.43 * 10^(-3)\ m


\lambda=11.43\ mm

time taken for a pulse that reflects off an object 3.0 m away to make a round trip


time = (\Delta x)/(\Delta v)


time = (2* 3)/(343)

t = 0.01749 s

t = 17.49 ms

User Sootah
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