Speed of Waves: Solving a Boating Problem

[Johnn17]

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..

 

[technicolour1]

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.

 

[Johnn17]

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?

 

[BruceW]

try drawing a sine wave, then it should become clear, since the (positive) peak happens once per wavelength.

 

[Johnn17]

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.

 

[technicolour1]

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.

 

[Johnn17]

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!