A sensor uses ultrasound to measure position and velocity of a moving cart in 1 dimension.

A sensor uses ultrasound to measure position and velocity of a moving cart in 1 dimension. It emits acoustic waves at 25 kHz and the speed of sound in air is 343 m/s. The maximum range of the cart from the wave emitter is 3 meters.

A: If the sensor wants to measure distance position accurately to within 1cm of the cart, what is the maximum velocity the cart can have and not change position by more than 1cm while the wave is traveling to and from the cart?

B: If the cart is moving at the max speed from part A, what will be the measured change in the frequency of the reflected wave coming back at the wave source? Calculate f’’ for the cart moving towards the sensor and away from the sensor.

C: If the sensor wants to measure velocity to within 1% of its max value, how accurately does it need to be able to measure the frequency of the reflected wave?

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Expert Solution

genius_generous answered 2 years ago

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