a fisherman noticed that his boat was lifted by the wter waves about once evry two seconds. He looked at the waves wnd estimated the length of a wave to be a 6cm. He also estimated the vertical distance between the highest point snd the lowest point of the wave to be 0.5m find the
a frequency of the wave
b. Speed of the water wave
C. Amplitude of the wave
D. Depth of the water assuming it is shallow water
What is the length of a wave mean? if you mean distance between peaks...that is wavelength, but 6cm?
To find the answers to the given questions, we need to use the formulas and concepts of wave properties. Let's walk through each question step by step:
a. Frequency of the wave:
The frequency (f) of a wave is the number of complete oscillations or cycles per second. In this case, the fisherman noticed that his boat was lifted by the water waves about once every two seconds. So, the frequency can be calculated using the formula:
frequency (f) = 1 / time period (T)
Since the time period is given as 2 seconds, we can substitute this value into the formula:
f = 1 / 2
f = 0.5 Hz
Therefore, the frequency of the wave is 0.5 Hz.
b. Speed of the water wave:
The speed (v) of a wave can be determined using the formula:
speed (v) = frequency (f) × wavelength (λ)
In this case, the wavelength (λ) is given as 6 cm. However, it is important to convert it to meters for consistency. Therefore, the wavelength is 6 cm or 0.06 m. Now, substitute the values into the formula:
v = 0.5 Hz × 0.06 m
v = 0.03 m/s
Therefore, the speed of the water wave is 0.03 m/s.
c. Amplitude of the wave:
The amplitude of a wave (A) is the maximum displacement or distance from the equilibrium position to the crest or trough of the wave. Here, the fisherman estimated the vertical distance between the highest point and the lowest point of the wave to be 0.5 m. So, the amplitude is 0.5 m.
Therefore, the amplitude of the wave is 0.5 m.
d. Depth of the water assuming it is shallow water:
To find the depth of the water (d), we need to use the formula for the relationship between wave speed, wavelength, frequency, and water depth in shallow water:
v = √(g × d)
Here, g represents the acceleration due to gravity (approximately 9.8 m/s²), which is a constant. Rearranging the formula, we can solve for d:
d = (v²) / (g)
Substitute the values of v and g:
d = (0.03 m/s)² / (9.8 m/s²)
d = 0.0009 m²/s² / (9.8 m/s²)
d = 0.0000918 m
Therefore, the depth of the water (assuming it is shallow water) is approximately 0.0000918 meters or 0.0918 mm.
Note: The given depth is very small because the waves have a small amplitude and short wavelength, indicating shallow water conditions.