Question

What is the mathematical relationship between celerity (speed), wavelength, and wave period for deep-water waves? For shallow-water waves?

a) Speed = Wavelength x Wave Period for deep-water waves. Speed = Square Root of (Wave Length x Gravity) for shallow-water waves.
b) Speed = Wave Period / Wavelength for deep-water waves. Speed = Wavelength / Wave Period for shallow-water waves.
c) Speed = Wave Period x Wavelength for deep-water waves. Speed = Wavelength x Wave Period for shallow-water waves.
d) Speed = Wavelength / Wave Period for deep-water waves. Speed = Wave Period / Wavelength for shallow-water waves.

Answer 1

For deep-water waves, wave speed (celerity) is found by dividing the wavelength by the wave period. For shallow-water waves, speed is calculated using the square root of the product of wavelength and gravity.

Step-by-step explanation:

The mathematical relationship between celerity (speed), wavelength, and wave period for different types of waves is pivotal in understanding wave motion. For deep-water waves, the wave speed (V) is the product of the frequency (f) and the wavelength (λ); this relationship is also expressed as speed being the wavelength divided by the wave period (T). The equation is V = λ / T. Conversely, for shallow-water waves, the speed is influenced by the depth of the water as well as the wavelength, with the relationship described by V = √(gλ) where g represents the acceleration due to gravity.