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Chapter 2: Q6E (page 497)

A fisherman notices that his boat is moving up and down periodically, owing to waves on the surface of the water. It takes \(2.5 s\)for the boat to travel from its highest point to its lowest, a total distance of\(0.53 m\). The fisherman sees that the wave crests are spaced \(4.8 m\)apart.

(a) How fast are the waves traveling?

(b) What is the amplitude of each wave?

(c) If the total vertical distance traveled by the boat were \(0.30 m\)but the other data remained the same, how would the answers to parts (a) and (b) change?

Short Answer

Expert verified

(a) \(0.96\,{m \mathord{\left/{\vphantom {m s}} \right.\\} s}\)

Step by step solution

01

Given data

Time required \(t = 2.5\,s\)

Wavelength \(\lambda = 4.8\,m\)

02

Concept/ Formula used

Formula:

\(\begin{array}{l}\lambda = \frac{v}{f}\\v = \frac{\lambda }{T}\end{array}\)

Where,\(\lambda \)is wavelength,\(v\)is velocity and\(f\)is frequency of wave

03

Calculation for wave speed

(a)

Time period

\(\begin{array}{c}T = 2t\\ = 2(2.5\,s)\\ = 5.0\,s\end{array}\) \(\begin{array}{c}v = \frac{{4.8\,m}}{{5.0\,s}}\\ = 0.96\,{m \mathord{\left/{\vphantom {m s}} \right.\\} s}\end{array}\)

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