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Chapter 11: Problem 18

Mathematical Description of a Wave You are swimming in the ocean as water waves with wavelength \(9.6 \mathrm{m}\) pass by. What is the closest distance that another swimmer could be so that his motion is exactly opposite yours (he goes up when you go down)?

Short Answer

Expert verified
Answer: The closest distance the other swimmer could be is 4.8 meters.

Step by step solution

01

Identify the phase difference

To find the distance when the motion of the second swimmer is exactly opposite to the first swimmer, we need to identify the phase difference between the two points. The second swimmer moves upward when the first swimmer moves downward, so the phase difference between their positions is half a period.
02

Calculate half the wavelength

Since the phase difference is half a period, we can find the distance by calculating half of the wavelength. Given the wavelength is \(9.6 \mathrm{m}\), half the wavelength can be calculated using the following formula: \(distance (d) = \dfrac{wavelength}{2}\)
03

Calculate the distance

Now we know that the distance can be found by dividing the wavelength by 2. Plugging in the given values, we get: \(d = \dfrac{9.6 \mathrm{m}}{2}\) \(d = 4.8 \mathrm{m}\) Thus, the closest distance that another swimmer could be so that his motion is exactly opposite yours is \(4.8 \mathrm{m}\).

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