Question

A child in an inner tube is bobbing up and down in the ocean and notices that after a wave crest passes, four more crests pass in a time of 42.4 s and the distance between the crests is 47 m.

If possible, determine the following properties for the wave. (If not possible, enter IMPOSSIBLE.)
(a) period s
(b) frequency Hz
(c) wavelength m
(d) speed m/s
(e) amplitude m

Answer 1

Period: 10.6 sec

Frequency = 0.094 Hz

Wavelength = 47 m

Speed = 4.418 m/s

Amplitude : Impossible

Step-by-step explanation:

Answer 2

period = 10.6 sec, frequency = 0.094 Hz, wavelength = 47 m and speed = 4.418 m/s.

Step-by-step explanation:

Given:

Four more crests pass in a time of 42.4 s and the distance between the crests is 47 m.

We have to determine five terms.

Lets start with one-one basis.

a.

Period = Time taken by a wave to pass though.

⇒
`P = (Total\ time)/(No.\ of\ waves)`

⇒
`P = (42.4)/(4)`

⇒
`P=10.6` s

b.

Frequency = Reciprocal of time period in Hertz.

⇒
`f=(1)/(T)`

⇒
`f=(1)/(10.6)`

⇒
`f=0.094` Hertz

c.

Wavelength = Distance between two consecutive trough and crest.

⇒
`\lambda = 47` m

d.

Speed (v) = Product of frequency and wavelength.

⇒
`v=f* \lambda`

⇒
`v=0.094* 47`

⇒
`v = 4.418` ms^-1

e.

Amplitude = The maximum displacement or half the distance from crest to trough.

⇒ Here it can't be determined.

⇒ Impossible.

So,

The period = 10.6 sec, frequency =0.094 Hz, wavelength = 47 m and speed = 4.418 m/s.