A woman is standing in the ocean, and she notices that after a wave crest passes by, five more crests pass in a time of 29.4 s. The distance between two successive crests is 31.4 m. What is the wave's (a) period, (b) frequency, (c) wavelength, and (d) speed

(a) 5.88 s

(b) 0.17 Hz

(c) 31.4 m

(d) 5.338 m/s

Explanation:

From the question,

(a) Period = time between successive crest = t/n ... Equation 1

where t = time, n = number of wave crest

Given: t = 29.4, n = 5

therefore,

Period (T) = 29.4/5 = 5.88 s.

(b) Frequency = 1/period

Frequency = 1/5.88

Frequency = 0.17 Hz.

(c) wavelength = distance between two successive crest = 31.4 m

(d) using,

v = λf ... Equation 2

Where v = speed, f = frequency, λ = wavelength

given: f = 0.17 Hz, λ = 31.4 m

Substitute into equation 2

v = 0.17 (31.4)

v = 5.338 m/s