Chapter 25, Problem 65A

While watching ocean waves at the dock of the bay, Otis notices that 10 waves pass beneath him in 30 seconds. He also notices that the crests of successive waves exactly coincide with the posts that are 5 meters apart. What are the period, frequency, wavelength, and speed of the ocean waves?

To determine

The time interval of the waves passing O.

Answer to Problem 65A

The period of the ocean waves is $\text{3 s}$

Explanation of Solution

Given:10 waves pass beneath O within $30\text{ s}$

Formula used:The period is calculated as the ratio of the total time taken and the number of cycles.

Calculation:The period of the ocean waves passing O is

  $\text{T = }\frac{30\text{ sec}}{10\text{ waves}}=3\text{ s}$

Conclusion: Thus, the period of the ocean waves is $\text{3 s}$

To determine

The frequency of the ocean waves.

Answer to Problem 65A

The frequency of the ocean waves is $0.33\text{ Hz}$

Explanation of Solution

Given: 10 waves pass beneath O within $30\text{ s}$ . The period of the ocean waves is $\text{3 s}$

Formula used: The frequency is calculated as the ratio of the number of cycles traveled in the time interval.

Calculation: The frequency of the ocean waves is

  $\text{f =}\frac{1}{\text{T}}=\frac{1}{3\text{ s}}=0.33\text{ Hz}$

Conclusion: Thus, the frequency of the ocean waves is $0.33\text{ Hz}$

To determine

The wavelength of the ocean waves.

Answer to Problem 65A

The wavelength of the ocean waves is $5\text{ m}$

Explanation of Solution

Given: 10 waves pass beneath O within $30\text{ s}$

Formula used: The wavelength is the distance between consecutive crests of a wave.

Calculation: The distance between the consecutive crests in the ocean wave is $5\text{ m}$

Conclusion: Thus, the wavelength of the ocean wave is $5\text{ m}$

To determine

The speed of the ocean waves.

Answer to Problem 65A

The speed of the ocean waves is $1.67\text{ m/s}$

Explanation of Solution

Given: The frequency of the ocean waves is $0.33\text{ Hz}$ . The wavelength of the ocean wave is $5\text{ m}$

Formula used: The speed of a wave is calculated as

  $\text{v = }\nu \times \lambda$

Calculation: The speed of the ocean wave is

  $\text{v =0}\text{.33 /s}\times \text{5 m}=1.67\text{ m/s}$

Conclusion: Thus, the speed of the ocean waves is $1.67\text{ m/s}$