Solving Beat Frequency Woes: Physics Exam Prep

[Batmaniac]

So I'm studying for my Physics exam tommorow and the damned Sound unit seems to always give me problems. Anyway I'm doing a review question relating to Beat Frequency and I just can't seem to figure out what to do. Here is the question and my sad attempt at it.

When a violin string is sounded together with a pitch pipe having a frequency of 256 Hz, 21 beats are heard in 3.00s. If the string is tightend, the beat frequency increases (not sure why this sentence is here or it's purpose). What is the original frequency of the violin string?

Well the first thing I did was calculate the Beat Frequency using the formula:

Beat Frequency = # of beats / time
Fb = 21 / 3s
Fb = 7Hz

I then proceeded to frequency of the violin string by doing this:

Frequency of violin = Frequency of pitch pipe +/- Fb
Fv = 256 Hz +/- 7Hz
Fv = 263 Hz or 249 Hz

To my knowledge those are the possible frequencies of the violin, but it's asking for the original frequency and I have no clue what to do. Any help would be greatly appreciated.

Thanks.

 

[chroot]

The sentence you noted provides what you need to select between the two possible values of Fv.

If you tighten the violin string, its pitch goes up. If the beat frequency increases, then it's becoming more out of tune. If you tighten the string and it becomes more out of tune, then it was producing too high a pitch to begin with.

- Warren

 

[Ouabache]

If you tighten the violin string, its pitch goes up. If the beat frequency increases, then it's becoming more out of tune. If you tighten the string and it becomes more out of tune, then it was producing too high a pitch to begin with.

- Warren

Good intuitive reasoning! I wonder did you play an instrument?
I play the guitar and mandolin and use this very relationship when tuning a string relative to a fork or to another string. I don't know many musicians who make use of this beating phenomena.

 

[Tide]

I don't know many musicians who make use of this beating phenomena.

They do! :)

 

[Ouabache]

They do! :)

LOL... They should, its not that hard.. Unfortunately many musicians rely either directly on their ear or use an electronic tuner. Of course to someone who understands physics, using frequency beating is obvious

 

[chroot]

I do play a couple of instruments. Every musician I've ever known has has an intuitive grasp of beat frequencies -- if you adjust your instrument and the beats get faster, you're getting more out of tune. To be in tune, you adjust the instrument until the period of beats is "infinite," or, at least, so long that it's no longer noticeable.

- Warren