The speed of a deep water wave with a wavelength ë is given approximately by v = (gë/2ð)1/2. Find the speed and frequency of a deep water wave with a wavelength of 5.5 m.
? m/s
? Hz
can someone get me started with a formula? I lost my book :(
The wave equation.
freq*wavelength=speed
No worries, I can help you with that! The formula you need is provided in the question itself: v = (gλ / (2π))^(1/2), where v represents the speed of the wave, g is the acceleration due to gravity (approximately 9.8 m/s^2), λ is the wavelength of the wave, and π is a mathematical constant approximately equal to 3.14159.
To find the speed and frequency of a deep water wave with a wavelength of 5.5 m, follow these steps:
Step 1: Plug in the given values into the formula. The wavelength, λ, in this case, is 5.5 m.
v = (gλ / (2π))^(1/2)
Step 2: Substitute g = 9.8 m/s^2 and λ = 5.5 m into the formula.
v = (9.8 * 5.5 / (2 * π))^(1/2)
Step 3: Simplify the equation within the parentheses.
v = (53.9 / 6.28)^(1/2)
Step 4: Evaluate the expression using a calculator.
v ≈ (8.59)^(1/2)
Step 5: Calculate the square root of 8.59.
v ≈ 2.93 m/s
So, the speed of the deep water wave is approximately 2.93 m/s.
To find the frequency of the wave, you can use the formula: f = v / λ, where f represents the frequency of the wave.
Step 6: Plug in the values of v = 2.93 m/s and λ = 5.5 m into the formula.
f = 2.93 / 5.5
Step 7: Calculate the value of f.
f ≈ 0.5327 Hz
Therefore, the frequency of the deep water wave is approximately 0.5327 Hz.