Question

A skipper on a boat notices wave crests passing the anchor chain every 5 seconds. the skipper estimates the distance between crests is 15 m. what is the speed of the water waves?

Answer 1

The speed of the water waves observed by the skipper is calculated by multiplying the frequency (0.2 Hz) with the wavelength (15 m), which results in a wave speed of 3 meters per second.

Step-by-step explanation:

To calculate the speed of the water waves that the skipper notices, we can use the formula for wave speed (v), which is the product of the frequency (f) and the wavelength (λ). The skipper mentions that wave crests pass every 5 seconds, so the frequency is 0.2 Hz (since frequency is the inverse of the time period: f = 1/T, where T is the time period). The distance between crests, which represents the wavelength, is 15 m.

Therefore, the speed of the waves can be found by multiplying the frequency by the wavelength:

v = f × λ

v = 0.2 Hz × 15 m

v = 3 m/s

The speed of the water waves observed by the skipper is 3 meters per second.

Answer 2

Because the crests occur every 5 seconds, the period is
T = 5 s.
By definition, the frequency is
f = 1/T = 1/5 = 0.2 Hz

The distance between crests is 15 m, therefore the wavelength is
λ = 15 m

By definition, the velocity, v, is
v = fλ
= (0.2 1/s)*(15 m)
= 3 m/s

Answer: 3 m/s