Concept explainers
A cowboy stands on horizontal ground between two parallel, vertical clifTs. He is not midway between the cliffs. Me fires a shot and hears its echoes. The second echo arrives 1.92 s after the first and 1.47 s before the third. Consider only the sound traveling parallel to the ground and reflecting from the cliffs, (a) What is the distance between the cliffs? (b) What If? If he can hear a fourth echo, how long after the third echo does it arrive?
(a)
The distance between the cliffs’s.
Answer to Problem 17.18P
The distance between the cliff’s is
Explanation of Solution
Given info: The time of the second echo is
The distance travelled by the echo is the sum of the distance travelled by the sound and the distance that is received after striking to the object to the transmitter.
The formula to calculate the time interval of the first echo is,
Here,
Substitute
Thus, the time interval of the first echo is
The formula to calculate the time interval of the second echo is,
Here,
Substitute
Thus, the time interval of the second echo is
The formula to calculate the time interval of the third echo is,
Here,
Substitute
Thus, the time interval of the third echo is
The formula to calculate the difference in time between the first and second echo is,
Here,
Substitute
The formula to calculate the difference in time between the second and third echo is,
Here,
Substitute
Thus, the value of time difference between the first and second echo is
Substitute
Conclusion:
Therefore, the distance between the cliff’s is
(b)
The time interval after which the third echo arrive.
Answer to Problem 17.18P
The time interval after which the third echo arrive is
Explanation of Solution
Given info: The time of the second echo is
The formula to calculate the time interval of the fourth echo is,
Here,
Substitute
Thus, the time interval of the fourth echo is
The formula to calculate the time interval of the third echo is,
Here,
Substitute
Thus, the time interval of the third echo is
The formula to calculate the difference in time between the third and fourth echo is,
Here,
Substitute
Substitute
Conclusion:
Therefore, the time interval after which the third echo arrive is
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Chapter 17 Solutions
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