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Chapter 16: Problem 37

How many times a minute does a boat bob up and down on ocean waves that have a wavelength of \(40.0 \mathrm{m}\) and a propagation speed of \(5.00 \mathrm{m} / \mathrm{s}\) ?

Short Answer

Expert verified
The boat bobs up and down approximately 7.5 times every minute on the ocean waves.

Step by step solution

01

Write down the given variables

The given variables in the problem are: Wavelength (位) = 40.0 m Propagation speed (v) = 5.00 m/s
02

Calculate the frequency of the ocean waves

Recall the formula that relates wave speed (v), frequency (f), and wavelength (位): \[v = f位\] We are given the wave speed and wavelength, and we need to find the frequency. Rearrange the formula to solve for frequency (f): \[f = \frac{v}{位}\] Now plug in the given values: \(f = \frac{5.00\ \text{m/s}}{40.0\ \text{m}}\)
03

Calculate the frequency

Divide the numbers to get the frequency value: \(f \approx 0.125\ \text{Hz}\) The frequency is approximately 0.125 Hz, meaning the waves pass by 0.125 times per second.
04

Convert frequency to bobs per minute

To find how many times a minute the boat bobs up and down, we need to convert the frequency in Hertz (Hz) to a value representing the number of times per minute. To do this, we can multiply the frequency by the number of seconds per minute: Bobs per minute = Frequency in Hz 脳 60 seconds/minute Bobs per minute = \(0.125\ \text{Hz} 脳 60\ \text{sec/min}\)
05

Calculate the final value

Multiply the numbers to get the final value: Bobs per minute 鈮� 7.5 So the boat bobs up and down approximately 7.5 times every minute on the ocean waves.

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