As water waves from the ocean approach a shallow beach, their wavelengths become shorter. Explain why.
v=fwavelength, frequency remains constant & velocity & wavelength decrease or increase w/ water depth.
Is that a reasonable answer or are they looking for something else?
Thanks :)
The speed is slower, but the same number have to pass you in a minute if you are sitting there watching. There is no storage closet for the waves.
In other words the same answer as for your earlier question.
L = v T
T is constant
v, the speed, decrease
so
L decreases
(it gets shorter and steeper and breeaks)
In deep water
v = constant * sqrt L
in shallow water
v = constant * sqrt (depth)
shallow water starts when the depth is about half the deep water wavelength. (It scrapes the bottom :)
Ok, that makes sense, thank you :)
Your answer is correct! As water waves travel from the deep ocean towards a shallow beach, their wavelengths become shorter. This phenomenon is known as wave shoaling.
The mathematical relationship that relates frequency (f), velocity (v), and wavelength (λ) of a wave is v = fλ. In this case, as the waves approach the shallow beach, the velocity of the waves decreases due to the friction between the waves and the ocean floor. This decrease in velocity causes the wavelength to decrease while the frequency remains constant.
So, your explanation that the velocity and wavelength decrease with water depth is an accurate and reasonable answer to why the wavelengths of water waves become shorter as they approach a shallow beach.
Your answer is quite reasonable! When water waves approach a shallow beach, their wavelengths become shorter. This phenomenon is known as wave shoaling. It occurs due to changes in water depth.
As you mentioned, the velocity of the water waves remains constant as they travel from the deeper ocean to the shallower beach. However, the wave undergoes changes in its speed as it encounters the changing water depth.
According to the wave equation v = f * λ, where v represents the velocity of the wave, f represents the frequency, and λ represents the wavelength, we can observe that both the velocity and frequency remain constant.
Since the velocity remains the same but the water depth decreases, the wave encounters a decrease in its wave speed. Remember that wave speed is equal to velocity divided by wavelength (v = f * λ). Therefore, if the wave speed decreases, the wavelength must also decrease to maintain the constant frequency.
In simpler terms, as the waves move from deeper water to the shallower beach, they encounter a decrease in the depth of the water. This change causes the wave to slow down, and consequently, the wavelength becomes shorter.
Hence, your explanation is on the right track!