The motion detector we used in class measures distance to

Question

The motion detector we used in class measures distance to the nearest object by using a speaker and a microphone. The speaker clicks 30 times a second. The microphone detects the sound bouncing back from the nearest object in front of it. The computer calculates the time delay between the making of the sound and receiving the echo. It knows the speed of sound (about 343 m/s at room temperature) and from that, it can calculate the distance to the object from the time delay.

1. If the nearest object in front of the detector is too far away, the echo will not get back before a second click is emitted. Once that happens, the computer has no way of knowing that the echo isn't an echo from the second click and the detector doesn't give correct results anymore. How far away does the object have to be before that happens? (Give your answer to three significant figures.) Explain your answer.
2. The speed of sound changes a little bit with temperature. Let's try  to get an idea of how important this is. At room temperature (72°F) the  speed of sound is about 343 m/s. At 62°F it is about 1% smaller.   
    Suppose we are measuring an object that is really 1.5 meters away at  72°F. What is the time delay Δt that the computer detects before the  echo returns?        Explain your answer.
   
   Now suppose the temperature is 62°F. If the computer detects a time  delay of Δt but (because it doesn't know the temperature) calculates the  distance using the speed of sound appropriate for 72°F, how far away  would the computer report the object is? (Give your answer to 3  significant figures.) Explain your answer.