Archives For Technology

A Musician on Mars

December 11, 2013 — 1 Comment


Welcome to Mars. As one of the first colonists on the fourth planet from the Sun, you endeavor to make it your new home. On Earth, you filled your time in numerous ways, but your real passion was music. Luckily, the Indian Space Research Organisation (ISRO) allowed you to bring your prized possession: a Steinway grand piano. Excited to play for the first time in months, you squeeze into your ISRO-issued space suit and wheel the piano onto the Martian surface. It’s noon near the equator. The temperature is around 25ºC (77ºF). You stretch out your arms, relax, and strike your first key. The sound is… quiet and out of tune. Assuming the piano needs to be retuned, you wheel it back into your pressurized vessel, take off your suit, and tune it yourself. Satisfied, you wheel the piano onto the surface again. The Martian surface is quiet, and you notice the colors of the sky are a lot redder than you had seen in NASA photographs. Again, you begin to play. It again sounds too quiet.

What is happening here? Why might a piano sound different when played on the Martian surface? This is a fairly involved question. Luckily, we are considering an instrument with taut strings rather than something that depends more upon atmospheric conditions than, say, a trombone or pipe organ. Furthermore, the equatorial temperature is Earth-like. Why, then, might a piano sound different on Mars?

When tuning and subsequently playing a piano, the frequency you perceive (or pitch) depends upon the tension, length, and mass of the strings within the piano. Since the temperature is about the same as before, and since you did not physically exchange the strings, these properties remain fairly constant. However, the fluid on the strings does play a role. Like any oscillator, the fluid in which it is immersed provides a load which will subsequently alter the frequency at which the oscillator resonates and by how much. On Mars, the atmosphere is more rarified, with a mean pressure of 600 Pa at the surface. Compare this with a pressure of over 100,000 Pa at sea level on Earth. This reduced loading by air results in a bias to slightly higher frequencies (or a higher pitch). If you retuned the piano in a pressurized cabin and then played the newly tuned piano on the Martian surface once again, it would still sound out of tune. A simple solution is to retune the piano while on the surface.

However, this is not the only problem with playing music on the Martian surface. Remember that Mars has a lower-pressure atmosphere. Sound, as you may recall, propagates as an oscillation of pressure in some medium (like air). If the mean pressure is lower, this presumably changes the ability of sound to propagate over longer distances. Without going into too many details here, what happens is that sound will not propagate very far on Mars, and there is an effect such that high frequencies are heavily attenuated. Before, the pitch was shifted slightly higher. Here, on the other hand, higher frequencies will sound softer than lower frequencies, and all frequencies will sound quieter. This means that not only does the piano sound out of tune, but it also sounds muted. The question of sound propagation is so interesting that an acoustics researcher simulated sound on Earth, Mars, and Titan. She found that a scream which may travel over one kilometer on Earth would only carry 14 meters on Mars!

Your out-of-tune, muted piano, probably wouldn’t be audible to a nearby audience on the Martian surface.

Keeping it Random

January 7, 2013 — Leave a comment

When iTunes “shuffle” was introduced, Apple received many complaints. It turns out that a number of songs were played many times, and customers felt that the randomness of this random shuffle algorithm was not truly random. Apple changed the algorithm, and it works a bit better now. However, their change actually made the process non-random. The previous iteration of the software was random. Why, then, did the complaints arise?

If you take a carton of toothpicks and throw them across the room in a truly random manner, you will notice that the toothpicks will start to form clusters. This “clumping” occurs due to the nature of a Poisson point process, or a Cox family of point processes. Simply put, the process tends to create clusters around certain locations or values when it is truly random. The same also occurred in World War II. The Germans were randomly bombing Britain. However, the randomness led to the same type of clustering one would see in iTunes. Certain targets were bombed more often than others. This led the British to think that the Germans had some strategy to their bombing when, in fact, the process was purely random. We tend to think that a random process would be evenly distributed, and when the reality defies our logic, we no longer see the randomness in the random process. Apple decided to change their algorithm to a less random but more evenly distributed one, and customers remained happy.

I can discuss different types of randomness fairly extensively, but I would rather touch upon two different types of random number generation. These are pseudo-random number generators and true random number generators. Pseudo-random number generators use mathematical formulae or tables to pull numbers that appear random. This process is efficient, and it is a deterministic, as opposed to a stochastic, one. The problem is that these generators are periodic and will tend to cycle through the same set of pseudo-random numbers. While they may be excellent for pulling random numbers on small scales, they fall prey to significant problems in large-scale simulations. The lack of true randomness creates artifacts in data and confounds proper analysis.

True random number generators, on the other hand, use real data. Typically, data from physical observations, such as weather patterns or radioactive decay, are extracted and used to generate random values. The lavarand generator, for example, used images of lava lamps to generate random numbers. These true random number generators are nondeterministic and do not suffer from the periodicity of pseudo-random number generators.

This distinction is important in the simulation of data. How can one best generate random numbers? If an internal clock is used to generate random numbers, but you are iterating through some code thousands of times, a periodicity dependent upon the computation time may result and generate artifacts. The use of atmospheric noise could overcome this, though pulling the data takes time and could slow down computation.

The world around us is filled with processes both random and nonrandom. It is a challenge to generate artificial random processes, and it is surprising that truly random processes often appear nonrandom to human observers.

A couple weeks ago, Felix Baumgartner set the record for the longest free fall, previously held by Captain Joseph Kittinger. To be more specific, Baumgartner dove from 39 kilometers in 2012, and Kittinger dove from 31 kilometers in 1960. However, Baumgartner traveled faster, with his total dive taking 17 seconds less than Kittinger’s. This was the true feat, as he reached 1,342 kilometers per hour, thus breaking the sound barrier.

At 39 kilometers, how high up was Baumgartner? This is 8% short of a full marathon, the distance of 4.4 Mount Everests stacked atop one another, and 3.6 times the greatest depth of the ocean. At this height, the temperature is only -25.6 C, the pressure is only 1/3 of that on the ground, and the effect of gravity was still 98-99% of what it would be at sea level. His maximum speed of 1.1 Mach (the speed of sound in dry air at 15 C and 1 atm) was just 13% short of the maximum speed of the X-1 rocket plane. In other words, he was moving very fast from an extreme height.

If you want to consider how this might affect a human, you must consider not speed, but acceleration. With the Stratos jump, it took Baumgartner 42 seconds to reach his terminal velocity. This is pretty quick. How did he do it? When in free-fall, we can consider two forces, drag and gravity. I noted above that the effects of gravity were reduced, but not by much, at this elevation (to 9.7 meters per second-squared, to be specific). The force of drag acting on a body is dependent upon its velocity. So, as you fall and gain speed, the effects of drag become greater. Eventually, drag force becomes great enough such that you cannot accelerate any further from gravity, and you reach terminal velocity. This is usually 25 m/s for most objects. However, Baumgartner was in the stratosphere. The air pressure, as I mentioned above, was only 0.33 that of what is at sea level. With such low air density, the effects of drag are reduced. The force of acceleration, relatively unchanged, provides a strong downward force (toward the Earth). This leads to a very high terminal velocity, one that can break the sound barrier. (I should note that the speed of sound is reduced at high elevation because sound propagation is dependent upon the density of the medium through which the wave travels.)

What does this have to do with acceleration, then? We know his speed was significant, and we know he did it quickly. According to the argument above, the only real force leading to acceleration is gravity, and we have an upper limit of 9.7-9.8 m/s^2. The numbers reported agree with this, with an average acceleration of about 8.8 m/s^2. Is this fast enough to hurt a human? Again, what matters is accelerationnot speed. This discussion started in WWI, where pilots reported vision problems with high-acceleration maneuvers. Today, we see it ranging from the design of rockets by NASA to safety reports in four-door sedans. If we look back at other human endeavors, we see a story of high acceleration. The now-retired shuttle missions accelerated astronauts to three times the force of gravity. The Apollo missions entered the atmosphere at six times the force of gravity upon their return home. However, the highest reported cases were with the Daisy Decelerator in the 1970s. Major Beeding was placed in this capsule, and he was decelerated at 83-times the force of gravity for approximately 0.04 seconds. He survived, emerging with a short period of shock and a bruised back. While I wouldn’t claim that most humans could survive such an extreme scenario, this demonstrates the importance of acceleration over total speed. With Baumgartner traveling at <1g (less than one times the force of gravity), this provided little danger.

Whether or not this provided a danger to the diver, it was an exciting watch. Whether or not it advanced our knowledge of the stratosphere, it gave me a fun topic for this blog post.