Speed of Waves: Solving a Boating Problem

In summary, the two people fishing from small boats 30m apart experience waves that cause their boats to bob up and down 15 times in 1 minute. One boat is on a crest while the other is in a trough with one full wave between them. The frequency is 0.25Hz and 1 wave occurs every 4 seconds. With a distance of 20m per wave, the speed of the waves is 5m/s. The number of waves between the boats is 1.5, with one full wave and one half wave.
  • #1
Johnn17
4
0

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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  • #2
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.
 
  • #3
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?
 
  • #4
try drawing a sine wave, then it should become clear, since the (positive) peak happens once per wavelength.
 
  • #5
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.
 
  • #6
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.
 
  • #7
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!
 

1. What is the speed of waves and how is it measured?

The speed of waves refers to how fast a wave is moving through a medium, such as water. It is typically measured in meters per second (m/s) or kilometers per hour (km/h). To measure the speed of waves, scientists use various tools such as a stopwatch or a wave meter. They also take into account factors such as wavelength and frequency to accurately calculate the speed.

2. How does the speed of waves affect boating?

The speed of waves can greatly impact boating, especially in rough waters. The faster the waves are moving, the more difficult it is for a boat to navigate through them. This can also cause a boat to experience more turbulence and potentially capsize. On the other hand, slower waves can make for a smoother and easier boating experience.

3. What factors can affect the speed of waves?

There are several factors that can affect the speed of waves, including the depth and temperature of the water, wind speed and direction, and the size and shape of the waves. The type of medium the wave is traveling through can also play a role, as waves move at different speeds in different materials.

4. How is the speed of waves related to the frequency and wavelength?

The speed of waves is directly related to both the frequency and wavelength. Frequency refers to the number of waves passing a certain point in a given time, while wavelength is the distance between two consecutive points on a wave. The higher the frequency, the shorter the wavelength, and the faster the wave will travel. This relationship is described by the equation: speed (v) = frequency (f) x wavelength (λ).

5. Can the speed of waves be changed?

Yes, the speed of waves can be changed. It can be altered by changing the properties of the medium it is traveling through, such as by changing the water's depth or temperature. Additionally, man-made structures such as breakwaters and jetties can also impact the speed of waves by altering their direction and intensity. However, the speed of waves is ultimately determined by natural factors such as wind and gravitational forces.

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