Chapter 18, Problem 1OQ

To determine

Rank the situations according to the intensity of sound at the receiver from highest to lowest.

Answer to Problem 1OQ

Ranking is $\text{d}>\text{a}=\text{c}>\text{b}$.

Explanation of Solution

Initially, the sliding section is moved a distance of $0.1\text{m}$, the extra path length the wave has to go through is $0.2\text{m=}\frac{\lambda }{4}$.

When the total length the sliding section is moved is $0.2\text{m}$, the extra path length becomes $0.4\text{m}=\frac{\lambda }{2}$. The interference shown is partial interference.

When the total length the sliding section is moved is $0.3\text{m}$, the extra path length becomes $\frac{3\lambda }{4}$. The interference shown is destructive interference.

When the total length the sliding section is moved is $0.4\text{m}$, one wavelength travels one wavelength farther. The interference shown is constructive interference.

Conclusion:

Thus, the ranking is $\text{d}>\text{a}=\text{c}>\text{b}$.