Speed of a Wave: Solve for V in 4.6m and 7.4s

[pmd28]

Homework Statement

A person fishing from a pier observes that five wave crests pass by in 7.4 s and estimates the distance between two successive crests to be 4.6 m. The timing starts with the first crest and ends with the fifth. What is the speed of the wave?

Homework Equations

f=1/T
v=λf

The Attempt at a Solution

I solved for the period first, so in 7.4 sec there was 5 waves. T=1.48
f=1/T=.6757
v=λf=4.6*(.6757)=3.11 m/s

I know my error has to do wit that sentence, "The timing starts with the first crest and ends with the fifth," but I'm not sure what I'm doing wrong.

 

[TSny]

Draw a sketch of a wave and number the crests 1 through 5. How many wavelengths are contained between 1 and 5?

 

[pmd28]

There are 4 wavelengths.

 

[TSny]

Good. So what should the period T actually be?

 

[Nickie]

Your attempt at a solution is correct, but you are missing a crucial step in your calculation. In order to find the speed of the wave, we need to use the formula v=λf, where v is the speed, λ is the wavelength, and f is the frequency. In this case, we have calculated the frequency to be 0.6757 Hz, but we still need to find the wavelength.

To find the wavelength, we need to consider the distance between two successive crests. Since five crests pass in 7.4 seconds, the distance between two successive crests is 4.6 m * 5 = 23 m. Therefore, the wavelength is 23 m.

Now, we can plug in the values into the formula v=λf to find the speed of the wave:

v=23 m * 0.6757 Hz = 15.52 m/s

Therefore, the speed of the wave is 15.52 m/s.

Remember, when solving scientific problems, it is important to carefully consider all given information and use the appropriate equations to find the correct solution. Keep up the good work!