A transverse wave is traveling through a canal. If the distance between two successive crests is 2.97 m and four crests of the wave pass a buoy along the direction of travel every 20.6 s, determine the following.
T = 20.6/4 = 5.15 seconds period between crests
wave goes 2.97 m in 5.15 seconds
speed of crest = 2.97/5.15 m/s
frequency = 1/T
since you did not include a question, I am guessing that is what you want
Oh buoy, looks like we've got some wave calculations to tackle! Let me wave my humor wand and help you out.
To determine the wavelength (distance between crests) of the transverse wave, we know that four crests pass a buoy in 20.6 seconds. So, we can calculate the time it takes for one crest to pass the buoy.
20.6 seconds / 4 crests = 5.15 seconds per crest
Now, we can use this time to find the speed of the wave. The speed of a wave can be calculated using the formula:
Speed = Wavelength / Time
Since we now know the time and want to find the wavelength:
Wavelength = Speed * Time
Now, let's solve for the wavelength:
Wavelength = 5.15 seconds/crest * 2.97 meters/crest
Wavelength ≈ 15.31655 meters
So, the wavelength of the transverse wave is approximately 15.31655 meters.
I hope the wave calculations didn't make you feel too sea-sick!
To determine the frequency and speed of the wave, we can use the formulas:
Frequency (f) = 1 / Time period (T)
Speed (v) = Frequency (f) x Wavelength (λ)
Step 1: Calculating the time period (T)
Given: Number of crests = 4
Time taken = 20.6 s
Time period (T) = Total time taken / Number of crests
= 20.6 s / 4
= 5.15 s
Step 2: Calculating the frequency (f)
Frequency (f) = 1 / Time period (T)
= 1 / 5.15 s
≈ 0.194 Hz
Step 3: Calculating the wavelength (λ)
Given: Distance between two successive crests = 2.97 m
Number of crests = 4
Total distance traveled by four crests = Distance between two crests x Number of crests
= 2.97 m x 4
= 11.88 m
Wavelength (λ) = Total distance traveled by four crests / Number of crests
= 11.88 m / 4
= 2.97 m
Step 4: Calculating the speed (v)
Speed (v) = Frequency (f) x Wavelength (λ)
= 0.194 Hz x 2.97 m
≈ 0.577 m/s
Therefore, the frequency of the wave is approximately 0.194 Hz and the speed of the wave is approximately 0.577 m/s.
To determine the frequency and speed of the wave, you can use the formulas:
1. Frequency (f) = 1 / Time period (T)
2. Wave speed (v) = Frequency (f) * Wavelength (λ)
First, let's find the time period (T) using the given information. We know that four crests pass a buoy every 20.6 s. Since a crest is equivalent to one wavelength, this means it takes 20.6 s for four wavelengths to pass the buoy.
Time period (T) = Total time / Number of wavelengths passing
T = 20.6 s / 4 = 5.15 s
Next, we can find the frequency (f) using the formula:
Frequency (f) = 1 / Time period (T)
f = 1 / 5.15 s ≈ 0.194 Hz
Now, let's find the wavelength (λ) using the given information. The distance between two successive crests is 2.97 m, which is the wavelength.
Wavelength (λ) = Distance between successive crests
λ = 2.97 m
Lastly, we can find the wave speed (v) using the formula:
Wave speed (v) = Frequency (f) * Wavelength (λ)
v = 0.194 Hz * 2.97 m ≈ 0.576 m/s
So, the frequency of the wave is approximately 0.194 Hz, and the speed of the wave is approximately 0.576 m/s.