Finding Wavelength and Velocity of an Ocean Wave.

In summary, we are trying to find the wavelength and velocity of an ocean wave based on known variables such as water depth, frequency, and amplitude. The equation to use is wavelength (m) x frequency (s-1) = velocity (m/s), with the known variable v representing velocity. However, there are still missing variables and equations that need to be solved using numerical methods. Simply measuring from crest to crest can give us the wavelength of the wave, but we need more information to find the velocity.
  • #1
Whatamiat
16
0

Homework Statement



Find Wavelength and Velocity of an Ocean Wave.

Known Variables:
Water Depth=300m
Frequency=8secs
Amplitude=3m


Homework Equations


Wavelength (m) X Frequency (s-1) = velocity (m/s)
ocwav.gif

v=velocity

The Attempt at a Solution



I have 2 missing variables for both of the above equations.
Am I missing a variable or equation?

Thanks.
 

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  • #2
To find the wavelength of an ocean wave you just need to measure from crest to crest.
 
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  • #3
cobrastrike said:
To find the wavelength of an ocean wave u just need to measure from crest to crest.

if only that were in the given data
 
  • #4
If you replace [tex]\lambda [/tex] in your equation according to
[tex]\lambda = \frac{v}{f}[/tex] where f is known
you will have an equation with only one unknown, v.
However this equation cannot be solved analytically but only by numerical methods.
 
  • #5


To find the wavelength and velocity of an ocean wave, you need to have at least two of the following variables: water depth, frequency, or amplitude. In this case, you have all three of these variables, so you can use the equation: wavelength (m) = velocity (m/s) / frequency (s-1).

To find the velocity, you can rearrange the equation to v = wavelength (m) x frequency (s-1). So, using the known variables, the wavelength would be (3m x 8s) = 24m, and the velocity would be 24m/s.

It is important to note that these calculations are based on ideal conditions and may not accurately represent the actual wavelength and velocity of an ocean wave. Other factors such as wind, currents, and temperature can affect these values.
 

1. What is the relationship between wavelength and velocity of an ocean wave?

The wavelength and velocity of an ocean wave are inversely proportional. This means that as the wavelength increases, the velocity decreases and vice versa. This relationship is known as the dispersion relation and is influenced by factors such as water depth and wind speed.

2. How do scientists measure the wavelength of an ocean wave?

The wavelength of an ocean wave is typically measured using a wave buoy or a specialized instrument called a wave staff. The buoy or wave staff records the frequency and height of the wave, which can then be used to calculate the wavelength using the dispersion relation.

3. What factors affect the velocity of an ocean wave?

The velocity of an ocean wave is affected by a variety of factors including water depth, wind speed, and the shape and size of the wave. The depth of the water plays a significant role in determining the speed of the wave, as shallow water causes the wave to slow down and steepen. Wind speed also influences the velocity of a wave, as stronger winds can create larger and faster waves.

4. How does the velocity of an ocean wave change as it approaches the shore?

As an ocean wave approaches the shore, its velocity decreases due to the decrease in water depth. This causes the wave to steepen and eventually break as it reaches the shoreline. The change in velocity also affects the wavelength, causing it to decrease and the wave to become shorter and more frequent.

5. Can the wavelength and velocity of an ocean wave be predicted?

While it is not possible to predict the exact wavelength and velocity of an individual ocean wave, scientists can make predictions based on factors such as wind speed, water depth, and wave height. These predictions can help to forecast ocean conditions and aid in activities such as surfing, boating, and coastal engineering.

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