Final answer:
To compute ranges corresponding to three echoes, we can use the formula r = vt, where r is the range, v is the velocity of the wave, and t is the time taken for the echo to return. The ranges can also be calculated if the ranges themselves are given. However, if no information about the time taken for the echo or the ranges is given, then additional information is needed to calculate the ranges.
Step-by-step explanation:
Radar is used to determine distances to various objects by measuring the round-trip time for an echo from the object. To compute ranges corresponding to three echoes, we can use the formula r = vt, where r is the range, v is the velocity of the wave, and t is the time taken for the echo to return. Let's calculate the ranges for each echo:
a) Using the formula r = vt:
Echo 1: r = (v)(t) = (speed of wave)(time for echo 1 to return) = (speed of wave)(150 m/s) = range of Echo 1
Echo 2: r = (speed of wave)(time for echo 2 to return) = (speed of wave)(300 m/s) = range of Echo 2
Echo 3: r = (speed of wave)(time for echo 3 to return) = (speed of wave)(450 m/s) = range of Echo 3
b) Ranges are independent of time:
Ranges can be determined using the formula r = vt, as explained in part a. The ranges do not depend on the specific time taken for the echo to return.
c) Echo 1: 150 m, Echo 2: 300 m, Echo 3: 450 m:
The range for each echo is already given: Echo 1 - 150 m, Echo 2 - 300 m, Echo 3 - 450 m.
d) Ranges cannot be calculated without additional information:
Ranges can be calculated using the formula r = vt, as explained in part a, or if the ranges are provided, as given in part c. However, if no information about the time taken for the echo to return or the ranges is given, then the ranges cannot be calculated without additional information.