A woman is standing in the ocean, and she notices that after a wave crest passes by, five more crests pass in a time of 68.0 s. The distance between two successive crests is 34.1 m. What is the wave's (a) period, (b) frequency, (c) wavelength, and (d) speed?
wave rock a boat in middle of a pond. the boat moves up and down 10 time in 20 s. what is the period of the wave ?
To find the wave's period, frequency, wavelength, and speed, we can use the following formulas:
(a) Period (T) = 1 / frequency (f)
(b) Frequency (f) = 1 / Period (T)
(c) Wavelength (λ) = speed (v) / frequency (f)
(d) Speed (v) = wavelength (λ) x frequency (f)
Let's calculate each step by step:
Step 1: Determine the number of wave crests passing in 68.0 seconds.
Given that after one wave crest passes, five more crests pass in a time of 68.0 seconds, the total number of wave crests passing in 68.0 seconds is: 1 + 5 = 6.
Step 2: Calculate the period.
The period (T) is the time it takes for one complete wave cycle.
Since we know that the number of wave crests passing is 6 and the time is 68.0 seconds, the period (T) is:
T = 68.0 s / 6 = 11.33 s (rounded to two decimal places).
Step 3: Calculate the frequency.
The frequency (f) is the reciprocal of the period (T).
So, the frequency (f) is:
f = 1 / T = 1 / 11.33 s = 0.088 Hz (rounded to three decimal places).
Step 4: Calculate the wavelength.
The wavelength (λ) is the distance between two successive wave crests.
Given that the distance between two successive crests is 34.1 m, the wavelength (λ) is:
λ = 34.1 m.
Step 5: Calculate the speed.
The speed (v) of the wave can be found using the formula:
v = λ x f.
Substituting the values, we have:
v = 34.1 m x 0.088 Hz = 2.99 m/s (rounded to two decimal places).
In summary:
(a) The wave's period is 11.33 seconds.
(b) The wave's frequency is 0.088 Hz.
(c) The wave's wavelength is 34.1 meters.
(d) The wave's speed is 2.99 m/s.
To find the wave's period, frequency, wavelength, and speed, we need to use the following formulas:
(a) Period (T) = 1 / Frequency (f)
(b) Frequency (f) = 1 / Period (T)
(c) Wavelength (λ) = Wave speed (v) / Frequency (f)
(d) Wave speed (v) = Wavelength (λ) x Frequency (f)
Given information:
- Five crests pass in a time of 68.0 s
- Distance between two successive crests = 34.1 m
Step 1: Finding the period (T)
To find the period, use the formula T = 1 / f, where f is the frequency.
Since five crests pass in a time of 68.0 s, the time taken for one wave is 68.0 s / 5.
Therefore, the period (T) can be calculated as T = 68.0 s / 5.
Step 2: Finding the frequency (f)
Using the formula f = 1 / T, substitute the value of the period (T) calculated in Step 1 to find the frequency (f).
Step 3: Finding the wavelength (λ)
To calculate the wavelength, use the formula λ = v / f, where v is the wave speed and f is the frequency.
Since the frequency (f) is calculated in Step 2, and the distance between two successive crests is given (34.1 m), we can substitute these values into the formula to find the wavelength (λ).
Step 4: Finding the wave speed (v)
Using the formula v = λ x f, substitute the value of the wavelength (λ) calculated in Step 3 and the frequency (f) calculated in Step 2.
By following these steps, we can find the wave's period, frequency, wavelength, and speed.
5T=68 => T=68/5=13.6 s
λ=34.1 m
v= λ/T
f=1/T