How do I translate periodic motion to translational motion?

[Eclair_de_XII]

Homework Statement

"Each piston of an engine makes a sharp sound every other revolution of the engine. (a) How fast is a race car going if its eight-cylinder engine emits a sound of frequency 750 Hz, given that the engine makes 2000 revolutions per kilometer? (b) At how many revolutions per minute is the engine rotating?"

Homework Equations

$f=750s^{-1}=750Hz=\frac{375}{\pi}\frac{rev}{s}$
$r=\frac{2000rev}{1km}$

The Attempt at a Solution

$v=\frac{f}{r}=\frac{1km}{2000rev}(\frac{375}{\pi}\frac{rev}{s})=\frac{3}{16\pi}\frac{km}{s}=\frac{675}{\pi}\frac{km}{hr}$

The book says that it's $v=340\frac{km}{hr}$. I don't understand what I am doing wrong.

 

[TomHart]

I'm not sure why you are using π. You just need to consider that one revolution of the engine results in the car moving a distance of 1/2000 km. And from the frequency of 750 Hz, you should be able to calculate how many revolutions the engine makes every second. From that you should be able to calculate the distance the car moves every second.

By the way, I did not get the same answer as the book, but I rushed my calculation.

 

[Eclair_de_XII]

And from the frequency of 750 Hz, you should be able to calculate how many revolutions the engine makes every second.

So $750 Hz$ is 750 cycles per second, which is, I take it, to be 750 revolutions per second?

 

[TomHart]

So 750Hz750Hz750 Hz is 750 cycles per second, which is, I take it, to be 750 revolutions per second?

I believe what they are implying is that it is a 4-stroke engine and that it makes a sharp sound when the spark plug fires causing combustion in a given cylinder. In other words, the combustion (and sharp sound) does not occur every revolution for each piston; it occurs every other revolution for each piston. But you have to remember that there are 8 pistons and that each piston is making a sharp sound every other revolution. And they are basically telling you that there are 750 sharp sounds every second. So based on that you can calculate the number of rotations (Edit: revolutions) the engine makes every second.

Edit 2: I think it would simplify it if you work in meters and seconds and then convert to km/hr at the end. That's just my personal preference though.

 

[Eclair_de_XII]

In other words, the combustion (and sharp sound) does not occur every revolution for each piston; it occurs every other revolution for each piston. But you have to remember that there are 8 pistons and that each piston is making a sharp sound every other revolution. And they are basically telling you that there are 750 sharp sounds every second.

Okay, so there is one sharp sound every two revolutions, then. There are eight revolutions, so four sharp sounds... I'm guessing: $v=\frac{750rev}{4s}(\frac{1km}{2000rev})(\frac{3600s}{1hr})=337.5\frac{km}{hr}$.

 

[TomHart]

That looks right to me. After looking at your result, I realize that my answer was wrong because in my mind I calculated 750/4 = 175. It should have been 187.5. Thus my error.

Good job!

 

[Eclair_de_XII]

Thanks. It's the first time I'm doing a frequency problem, and you've been a great help.