A cork on the surface of a pond bobs up and down two times per second on ripples having a wavelength of 7.30 cm. If the cork is 12.0 m from shore, how long does it take a ripple passing the cork to reach the shore?
12m / 7.3*10^-2m/cy = 164.38 cycles.
164.38cy / 2cy/s = 82.2s.
To find out the time it takes for a ripple to reach the shore, we need to calculate the period (T) of the ripples first.
The period of a wave is the time it takes for one complete wavelength to pass a given point.
Given:
Frequency (f) of the ripples = 2 Hz (since the cork bobs up and down two times per second)
Wavelength (λ) of the ripples = 7.30 cm
We know that wave velocity (v) is equal to the product of frequency and wavelength:
v = f * λ
Let's convert the wavelength to meters for consistency:
λ = 7.30 cm = 0.0730 m
Now we can calculate the wave velocity:
v = (2 Hz) * (0.0730 m) = 0.146 m/s
The formula for wave velocity is:
v = distance / time, where distance is the distance from the cork to the shore.
Let's solve for time (T):
T = distance / v
Substituting the values:
T = (12.0 m) / (0.146 m/s)
Calculating the value:
T = 82.191 seconds
Therefore, it would take approximately 82.191 seconds for a ripple passing the cork to reach the shore.
To determine the time it takes for a ripple to reach the shore, we can use the wave equation:
v = λf
Where:
v = velocity of the wave
λ = wavelength of the wave
f = frequency of the wave
In this case, the frequency of the wave is given as 2 times per second. We can calculate the velocity of the wave by multiplying the frequency by the wavelength:
v = (2 waves/s) * (7.30 cm/wave) [convert cm to meters by dividing by 100]
v = (2 * 7.30 cm) / (100 cm/m)
v = 0.146 m/s
Now, we can calculate the time it takes for the ripple to reach the shore, which is the distance from the cork to the shore divided by the velocity of the wave:
t = distance / velocity
t = 12.0 m / 0.146 m/s
t ≈ 82.19 seconds
Therefore, it takes approximately 82.19 seconds for a ripple to pass the cork and reach the shore.