Question

A container ship is traveling westward at a speed of 5 m/s. The waves on the surface of the ocean have a wavelength of 40 m and are traveling eastward at a speed of 16.5 m/s. At what time intervals does the ship encounter the crest of a wave?
a. 1.9

b. 2.3

c. 1.4

d. 2.2

Answer 1

(16.5 m/s + 5 m/s) ÷ (40 m) = 0.5375 Hz

1 ÷ 0.5375 Hz = 1.86 s

round up and you get 1.9 s, so the answer would be A.

Answer 2

Answer: Option (a) is the correct answer.

Explanation:

It is known that frequency is velocity or speed divided by wavelength.

Mathematically,       f = $\frac{v}{\lambda}$

where          v = speed or velocity

                 $\lambda$ = wavelength

Therefore, total speed of ship will be (5 + 16.5) m/s = 21.5 m/s. Firstly calculate the frequency as follows.

                       f = $\frac{v}{\lambda}$

                         = $\frac{21.5 m/s}{40 m}$    

                         = 0.537 Hz

Also it is known that frequency is inversely proportional time. Hence calculate the time interval of ship encountering the crest of a wave as follows.

                      f = $\frac{1}{T}$

 or,               T = $\frac{1}{f}$

                        = $\frac{1}{0.537}$

                        = 1.86 s

                        = 1.9 (approx)

Thus, we can conclude that time intervals at which the ship encounter the crest of a wave is 1.9 s.