In the diagram below, a water wave having a speed of 0.25 meter per second causes a cork
to move up and down 4.0 times in 8.0 seconds. What is the wavelength of the wave
is it 2m?
No, 0.50m.
one wave in 2 seconds
distance = speed * time = .25 *2 = .5
To find the wavelength of the wave, we need to use the equation:
Wave speed (v) = frequency (f) × wavelength (λ)
Given that the speed is 0.25 m/s, we can use the formula to calculate the frequency:
v = f × λ
rearranging the formula gives us:
λ = v / f
We know that the cork moves up and down 4.0 times in 8.0 seconds, which means that the frequency is 4.0/8.0 = 0.5 Hz.
Now, substituting the values into the equation:
λ = 0.25 m/s / 0.5 Hz
Calculating:
λ = 0.5 meters
Therefore, the wavelength of the wave is 0.5 meters, not 2 meters as mentioned in your question.
To calculate the wavelength of the wave, we can use the formula:
wavelength = speed / frequency
Given that the speed of the wave is 0.25 m/s and the cork moves up and down 4.0 times in 8.0 seconds, we need to determine the frequency first.
The frequency of a wave is defined as the number of oscillations (or cycles) per unit of time. In this case, the cork moving up and down is equivalent to one cycle.
So, the frequency of the wave can be calculated by dividing the number of cycles (4.0) by the time taken (8.0 seconds):
frequency = 4.0 cycles / 8.0 seconds = 0.5 Hz (Hertz)
Now that we have determined the frequency, we can calculate the wavelength:
wavelength = speed / frequency
wavelength = 0.25 m/s / 0.5 Hz
wavelength = 0.5 meters
Therefore, the wavelength of the wave is 0.5 meters, not 2 meters.