Guitar String Vibrations: Freq 437 Hz, Distance 235m

[petern]

Homework Statement

A guitar string is set in vibrations at a frequency of 437 Hz. How many vibrations did the guitar's string make while the sound propagated 235 m in the air?

Homework Equations

V = wavelegth x freq.

The Attempt at a Solution

I figured out that you do 437 Hz x 235 m = 102695 m/s. 102695 / 343 = 299.4 vibrations.

Can anyone explain how this works? I thought vibration was the frequency. I don't understand how the vibration represents how many times faster than the speed of sound it is.

 

[Jakell]

first you want to figure out how long it takes the sound to travel the 235 meters. if you know that, you can use the frequency to figure out how many times the string vibrates in that period.

 

[Tedjn]

The vibration is the frequency. What you did gave you the right answer, but it was done in the wrong order. Following what Jakell said, you would want to first find the time it takes sound to travel 235 meters, which is (235 m)/(343 m/s) [if you are using 343 m/s for speed of sound]. Then you would use the frequency. You end up with the same operations, hence the same answer.

 

[petern]

How would I make a working equation for that? I currently have vibration = (x/v) x f. I used x = xo + vt but I don't know which eq. to use to add the f in.

 

[Tedjn]

What equation do you mean? You have one: # of vibrations = (x/v) * f