Speed of Waves: Solving a Boating Problem

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Homework Help Overview

The problem involves two boats bobbing in water due to passing waves, with a specific focus on determining the speed of these waves based on their positions and the frequency of their motion. The subject area includes wave mechanics and basic principles of frequency and wavelength.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between the distance between the boats and the number of waves present. There is an attempt to calculate the speed of the waves using frequency and distance, with some questioning the visualization of wave positions.

Discussion Status

Some participants have provided guidance on visualizing the wave structure between the boats, suggesting that drawing a sine wave could clarify the situation. There is an ongoing exploration of how to accurately represent the number of waves between the boats, with some expressing confusion about the concept of 1.5 waves.

Contextual Notes

Participants are working within the constraints of the problem statement, which specifies the distance between the boats and the frequency of their motion. There is an emphasis on understanding the wave properties without providing a definitive solution.

Johnn17
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Homework Statement



Two people are fishing from small boats located 30m apart. Waves pass through the water and each person's boat bobs up and down 15 times in 1 minute. At a time when one boat is on a crest, the other boat is in a trough, and there is one crest between the two boats. What is the speed of the waves?

Homework Equations


The Attempt at a Solution



Found the frequency, 0.25Hz, and then want to use dxm / L = m λ ... Not sure what the Xm would be though, or L for that matter. It must not be the correct equation..
 
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Hi Johnn,

If one boat is on a trough while the other is on a peak with one peak between them, there must be 1.5 waves between the boats. Since the boats are 30m apart, 1 wave = 30m/1.5 = 20m (If you draw it, you can tell that a full wave occurs at 2/3 the distance between them. Since 0.25 waves occur every second (as you calculated with the frequency), 1 wave happens every 4 seconds. Since 1 wave is 20m, the speed is v=d/t = 20m/4s = 5m/s.
 
technicolour1 said:
Hi Johnn,

If one boat is on a trough while the other is on a peak with one peak between them, there must be 1.5 waves between the boats. Since the boats are 30m apart, 1 wave = 30m/1.5 = 20m (If you draw it, you can tell that a full wave occurs at 2/3 the distance between them. Since 0.25 waves occur every second (as you calculated with the frequency), 1 wave happens every 4 seconds. Since 1 wave is 20m, the speed is v=d/t = 20m/4s = 5m/s.

Thanks for the quick response, it makes sense the answer, but for some reason I can't understand how there is 1.5 waves between the boat? I guess I just can't visualize (or draw) this situation. Any recommendations?
 
try drawing a sine wave, then it should become clear, since the (positive) peak happens once per wavelength.
 
BruceW said:
try drawing a sine wave, then it should become clear, since the (positive) peak happens once per wavelength.

Doing this would make it look like they destructively interfere all the time... To me at least.
 
Consider the boat that is on a peak. There is one full wave between the peak which this boat is on and the peak between the two boats. Then, from the peak between the boats until the trough that the other boat is on, there is one half wave. That is a total of 1.5 waves. Hopefully this is helpful.
 
technicolour1 said:
Consider the boat that is on a peak. There is one full wave between the peak which this boat is on and the peak between the two boats. Then, from the peak between the boats until the trough that the other boat is on, there is one half wave. That is a total of 1.5 waves. Hopefully this is helpful.

Ah yeah that makes sense, I was just drawing it strangely. Thanks for the help!
 

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