Area under a frequency vs wavelength graph?

[JosephTraverso2]

Homework Statement

Hi Everyone,

So I'm doing writing up my weekly physics lab report and I had an idea to better present my findings. I have a chart displaying the frequencies of numerous tuning forks as well as their experimentally determined wavelengths and I have to find the speed of sound within our classroom. If I plot a frequency vs. time graph, can I obtain the average speed of sound by finding the area under the graph or am I mistaken? Thank you for your time.

Homework Equations

V = F * ƛ

 

[DaveE]

This may be a good time to think about the dimensions or units of measurement of the quantities in your equations (i.e. dimensional analysis).
For example, in your equation V = F * λ. The dimensions of λ are meters (feet, miles, etc.). The dimensions of F are 1/seconds (hertz, "per hour", etc). When you multiply them together you get meters/seconds, which are the dimensions of velocity. So this all works out ok, you expected a velocity out of that equation.
Now look at the area under a frequency versus time curve. For dimensional analysis, finding the area under a curve will have the units of the two axes multiplied together. For example, if you graph the velocity of a car versus time the area would be the distance traveled; eg. miles/hour * hours = miles.
So for your proposal of the area under the graph of frequency versus time what would the resulting dimensions be? Are those the dimensions of the answer you expect (or want)?

 

[JosephTraverso2]

If I plot a frequency vs. time graph

My mistake I meant frequency vs. Wavelength graph.

 

[JosephTraverso2]

I went ahead and did a definite integral on my calculator and got V sound = 223.03 meters/second. Why is this so inaccurate?

 

[DaveE]

Yes, those units are correct. This doesn't necessary mean your equation is right, of course. This method is good for spotting poorly constructed equations, not so good at proving if the equation is correct. For example, it is useless in finding if you should or shouldn't multiply something by π, which has the same dimensions of 1, 2, e, etc.

 

[JosephTraverso2]

Yes, those units are correct. This doesn't necessary mean your equation is right, of course. This method is good for spotting poorly constructed equations, not so good at proving if the equation is correct. For example, it is useless in finding if you should or shouldn't multiply something by π, which has the same dimensions of 1, 2, e, etc.

Ok great, thank you for answering all my questions. Have a nice day!

 

[DaveE]

I am assuming that you have a pair of measurements for each tuning fork (F, λ), so your graph has a few distinct points, one for each tuning fork. What you are trying to do is find the speed of sound using the formula you were given V = F * λ? What if you only had one tuning fork to measure, could you do it with those data?

 

[JosephTraverso2]

What you are trying to do is find the speed of sound using the formula you were given V = F * λ?

I'm sorry can you retype this? I cannot understand what you are trying to say.

 

[DaveE]

I was just trying to understand the question you were asked to solve and what your data and graph are (and why you have a graph of the data).

 

[JosephTraverso2]

I was just trying to understand the question you were asked to solve and what your data and graph are (and why you have a graph of the data).

the question I have is "What is the speed of sound within our classroom" and the data I got was this (Frequency in hertz on the Y axis and Wavelength on the X-axis in meters)