Concept explainers
In figure OQ18.1 (page 566), a sound wave of wave-lenght 0.8 m divides into two equal parts that recombine to interfere constructively, with the original difference between their path lengths being |r2 – r1| = 0.8 m. Rank the following situations according to the intensity of sound at the receiver from the highest to the lowest. Assume the tube walls absorb no sound energy. Give equal ranks to situations in which the intensity is equal.
(a) From its original position, the sliding section is moved out by 0.1 m. (b) Next it slides out an additional 0.1 m. (c) It slides out still another 0.1 m. (d) It slides out 0.1 m more.
The ranking of the situations according to the intensity of sound at the receiver in descending order.
Answer to Problem 18.1OQ
The ranking of the situations according to the intensity of sound at the receiver in descending order is
Explanation of Solution
Given info: The wavelength of the sound wave is
Write the expression for the intensity heard by the receiver.
Here,
For Case (a);
The section is moved out by
The path length
Thus, the value of
Write the expression for phase difference,
Substitute
Thus, the value of
Substitute
Thus the value of
For Case (b);
The section is again moved out by
The path length
Thus, the value of
Write the expression for phase difference,
Substitute
Thus, the value of
Substitute
Thus the value of
For Case (c);
The section is again moved out by
The path length
Thus, the value of
Write the expression for phase difference,
Substitute
Thus, the value of
Substitute
Thus, the value of
For Case (d);
The section is again moved out by
The path length
Thus, the value of
Write the expression for phase difference,
Substitute
Thus, the value of
Substitute
Thus, the value of
The ranking of the intensity of each case is,
Conclusion:
Therefore, the ranking of the situations according to the intensity of sound at the receiver in descending order is
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Chapter 18 Solutions
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