Ocean Currents

NASA’s Perpetual Ocean visualizations are excellent animations of the oceans’ surface currents.

Sound Waves: Calculating Wavelength and Frequency

One of my physics students is working on a project to demonstrate interference in sound waves, so I generated a few sound files with different wavelengths for her to experiment with.

A sound wave with a frequency of 347 cycles per second (347 Hz), which has a wavelength of approximately 1 meter. Waveform captured using the WaveWindow program.

Using SoX, you can generate waves by inputing the frequency you want (using the synth command). The frequency ( $f$ ) depends on the wavelength ( $\lambda$ ) and speed ( $v$ ) of the sound waves through air.

$f = \frac{v}{\lambda}$

The speed of sound through the air depends on the temperature (it’s a linear relationship). Hyperphysics has a nice Speed of Sound in Air calculator, which tells me that at room temperature (about 25 ºC):

Speed of Sound in Air:
v = 347 m/s

Using the formula above (or sengpielaudio’s wave calculator) we can calculate the frequency we need for any wavelength.

For example, if we wanted a 2 meter wavelength:

$f = \frac{v}{\lambda}$

$f = \frac{347 \; \textrm{m/s}}{2 \;\textrm{m}}$

$f = 173.5 \; s^{-1}$

Which sounds like this: 2m.mp3. (Note that 1 cycle per second equals 1 hertz, so 173.5 s^-1 = 173.5 Hz).

The tone files I’ve created are below (the ones greater than 1 m may work best, but I’ve included the others for completeness):

Wavelength	Frequency	Sound File (mp3)
0.1 m	3470 Hz	10cm.mp3
0.25 m	1388 Hz	25cm.mp3
0.5 m	694 Hz	50cm.mp3
1 m	347 Hz	1m.mpg
2 m	173.5 Hz	2m.mp3
3 m	116 Hz	3m.mp3

Notes

SoX

The SoX command to create the 2 m sound file (that lasts for 60 seconds) is:

 > sox -n 2m.mp3 synth 60 sin 173.5

On the SoX manual page, look up the synth command.

WaveWindow

WaveWindow is a nice, shareware ($12) oscilloscope for the Mac, though it does not show the longer wavelengths very nicely.

Curious Correlations

The Correlated website asks people different, apparently unrelated questions every day and mines the data for unexpected patterns.

In general, 72 percent of people are fans of the serial comma. But among those who prefer Tau as the circle constant over Pi, 90 percent are fans of the serial comma.

— ᔥ Correlated.org: March 23’s Correlation.

Two sets of data are said to be correlated when there is a relationship between them: the height of a fall is correlated to the number of bones broken; the temperature of the water is correlated to the amount of time the beaker sits on the hot plate (see here).

snow-T_data-0643 — A positive correlation between the time (x-axis) and the temperature (y-axis).

In fact, if we can come up with a line that matches the trend, we can figure out how good the trend is.

The first thing to try is usually a straight line, using a linear regression, which is pretty easy to do with Excel. I put the data from the graph above into Excel (melting-snow-experiment.xls) and plotted a linear regression for only the highlighted data points that seem to follow a nice, linear trend.

melting-snow-graph-2 — Correlation between temperature (y) and time (x) for the highlighted (red) data points.

You’ll notice on the top right corner of the graph two things: the equation of the line and the R², regression coefficient, that tells how good the correlation is.

The equation of the line is:

y = 4.4945 x – 23.65

which can be used to predict the temperature where the data-points are missing (y is the temperature and x is the time).

You’ll observe that the slope of the line is about 4.5 ºC/min. I had my students draw trendlines by hand, and they came up with slopes between 4.35 and 5, depending on the data points they used.

The regression coefficient tells how well your data line up. The better they line up the better the correlation. A perfect match, with all points on the line, will have a regression coefficient value of 1.0. Our regression coefficient is 0.9939, which is pretty good.

If we introduce a little random error to all the data points, we’d reduce the regression coefficient like this (where R² is now 0.831):

snow-melting-randomized — Adding in some random error causes the data to scatter more, making for a worse correlation. The black dots are the original data, while the red dots include some random error.

The correlation trend lines don’t just have to go up. Some things are negatively correlated — when one goes up the other goes down — such as the relationship between the number of hours spent watching TV and students’ grades.

negative-correlation — The negative correlation between grades and TV watching. Image: ᔥ Lanthier (2002).

Correlation versus Causation

However, just because two things are correlated does not mean that one causes the other.

A jar of water on a hot-plate will see its temperature rise with time because heat is transferred (via conduction) from the hot-plate to the water.

On the other hand, while it might seem reasonable that more TV might take time away from studying, resulting in poorer grades, it might be that students who score poorly are demoralized and so spend more time watching TV; what causes what is unclear — these two things might not be related at all.

Which brings us back to the Correlated.org website. They’re collecting a lot of seemingly random data and just trying to see what things match up.

Curiously, many scientists do this all the time — typically using a technique called multiple regression. Understandably, others are more than a little skeptical. The key problem is that people too easily leap from seeing a correlation to assuming that one thing causes the other.

Hat Tips (↬) and Vias (ᔥ): The Subtler Side of Citation on the Web

ᔥ Curator’s Code ↬ On The Media

The Curator’s Code suggests symbols to help give credit for things on the web.

Vias (ᔥ) go to the link where you actually found the information you’re using,
Hat tips (↬) credit the sites that pointed you in the right direction.

For example, I found out about the Curator’s Code on the On The Media program, so I should give them a hat tip like this:

↬ On The Media

I got the actual symbols off the Curator’s Code website so I could say the symbols come via them:

ᔥ Curator’s Code

My standard form will be to stick these reference types at the bottom of each post or citation when they’re applicable. Like so:

ᔥ Curator’s Code ↬ On The Media

Spring is Coming Earlier

spring-early — The average change in the date of "first leaf" in the United States. Note that states farther to the north have seen greater change. Image from the interactive by Climate Central.

In Missouri, between 1981 and 2010 the average date at which trees first showed their leaves was two days earlier than the average between 1951 and 1980, according to this graphic by Climate Central.

You’ll also note the north-south trend, where change is greater as you go north. Most models predict that global warming/climate change due to increasing carbon dioxide will result in bigger changes as you get toward the poles.

The map is based on data from the National Phenology Network. The National Phenology Network has a good educational resource page, as well as access to their datasets.

spring-early-mo — Spring has been coming two days earlier (on average) in Missouri. Image from Climate Central.

The End of the Earth

The Earth will end with fire, non-metaphorically. It will be consumed when the sun expands as it runs out of fuel, 5 billion years from now.