The distance between successive crests in a series of water waves is 5.0m; the crests travel 8.6m in 5.0s . Calculate the frequency of a block of wood bobbing up and down in the water
wavelength = speed * period
5 = (8.6/5) * period
period = 25/8.6 = 2.9 seconds
frequency = 1/period = .344 Hz
Genius answer
Why did the block of wood join the water waves? Because it wanted to show off its bobbing skills, of course! Let's calculate the frequency to see how good this block of wood really is.
The distance between successive crests in the water waves is 5.0m. So, in one complete wave cycle, the block of wood would bob up and down a distance of 5.0m.
The crests travel 8.6m in 5.0s. To find the time it takes for one wave cycle, we need to calculate the time it takes for the crests to travel 5.0m.
8.6m / 5.0s = 1.72 m/s
Now, we can calculate the time it takes for the block of wood to complete one cycle:
5.0m / 1.72 m/s = 2.91s
The frequency of the block of wood bobbing up and down is the inverse of this time:
1 / 2.91s ≈ 0.34 Hz
So, the frequency of the block of wood is approximately 0.34 Hz. That's a pretty decent bobbing frequency considering it's just a block of wood!
To calculate the frequency of a block of wood bobbing up and down in the water, we need to use the formula:
Frequency = 1 / Time Period
The time period can be determined by finding the time it takes for one complete wave to pass, which is equal to the time it takes for one crest to travel a distance equal to the distance between successive crests.
Given:
Distance between crests (wavelength) = 5.0m
Distance traveled in 5.0s (wave speed) = 8.6m
Since the wave speed is equal to the wavelength divided by the time period:
Wave speed = Wavelength / Time Period
We can rearrange this formula to find the time period:
Time Period = Wavelength / Wave Speed
Substituting the given values:
Time Period = 5.0m / 8.6m/s = 0.581s
Finally, we can find the frequency by taking the reciprocal of the time period:
Frequency = 1 / 0.581s ≈ 1.72 Hz
Therefore, the frequency of the block of wood bobbing up and down in the water is approximately 1.72 Hz.
To calculate the frequency of the block of wood bobbing up and down in the water, we can use the formula:
Frequency (f) = Speed (v) / Wavelength (λ)
Given:
- The distance between successive crests (wavelength) = 5.0 m
- The distance traveled by the crests (speed) = 8.6 m
- The time taken for this distance (time) = 5.0 s
To find the speed (v), we divide the distance traveled by the time taken:
Speed (v) = Distance (d) / Time (t)
= 8.6 m / 5.0 s
Next, we need to determine the number of wavelength cycles that occurred during this distance. We can find this by dividing the distance traveled by the wavelength:
Number of cycles (n) = Distance (d) / Wavelength (λ)
= 8.6 m / 5.0 m
Now, we can calculate the frequency using the formula:
Frequency (f) = Number of cycles (n) / Time (t)
= n / t
Let's substitute the values we have:
Frequency (f) = (8.6 m / 5.0 m) / 5.0 s
Now we can calculate the frequency:
f = 1.72 / 5.0
f ≈ 0.34 Hz
Therefore, the frequency of the block of wood bobbing up and down in the water is approximately 0.34 Hz.