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Would a guitar sound the same on a space station?
Category: Space
Published: January 29, 2016
By: Christopher S. Baird, author of The Top 50 Science Questions with Surprising Answers and physics professor at West Texas A&M University
Yes. Since a space station typically contains regular air at normal pressure in order to keep the humans comfortable, the sounds created by playing a guitar will be the same as on earth. The weightless environment inside a space station has no effect on the guitar's ability to create sound. Sound is created by the strings and body of a guitar when they vibrate quickly after being plucked. These vibrations knock against the air, causing the air to vibrate quickly, which we humans experience as sound. The guitar strings vibrate back and forth so quickly when plucked because of a tug-of-war between two effects: the tension in the string and the inertia of the string.
The tension in the string is a force which tends to pull the string from a stretched, bent shape back to a compact, straight shape. In contrast, the inertia of the string's mass causes a string that is moving to continue moving, even after it has reached the compact, straight shape. Inertia therefore causes the moving string to overshoot the straight shape that the tension is trying to get it into. A cycle therefore ensues involving the tension in the string repeatedly trying to get the string straight again, and the inertia of the string repeatedly causing the string to get bent again. This cycling motion of the string happens so quickly that humans see it as a blurry vibration. There is one more important parameter involved, which is the length of the string. The length of the string determines how much the string can be deformed during its vibration, so it also has an effect on the vibration of the string.
Assume that the sound created by a guitar string is a single pitch. It really isn't, but this is a good enough approximation for our purposes. Applying the concepts mentioned above, we see that the pitch of the sound that is generated depends on the string's length L, the string's total mass M, and the string's tension T. Scientifically, what we call the pitch of a sound is actually its frequency of vibration, i.e. its number of vibrations per second. A string with a higher tension will snap back more quickly toward the straight shape and thus complete more cycles of vibration each second. For this reason, we can conclude that the sound's frequency is proportional to the string's tension. Also, a string with more mass will have more inertia. It will therefore overshoot the straight shape more and require more time to be pulled back toward the straight shape. Therefore, we conclude that the frequency is inversely proportional to the string's mass. Lastly, a longer stringer is more able to be deformed, and thus will take longer to return to the straight shape. Therefore, we conclude that the frequency is inversely proportional to the length of the string. Assembling these conclusions, we should expect the frequency of the sound created by a guitar string to be proportional to T/LM. In fact, the frequency obeys the equation f2 = T/4LM.
Notice that no where in this equation does gravity ever come into play. Therefore, the sound produced by a guitar string sounds the same no matter how strong gravity is (as long as gravity is not so strong as to break or damage the string). I said that the vibrating string is continually trying to return to the straight shape. This is not strictly true. More accurately, a vibrating string is continually trying to return to its equilibrium state. For a string on a guitar, its equilibrium state is effectively a straight shape. In contrast, for a heavy power line strung between two poles, its equilibrium state is a downward drooping arch. The power line can indeed vibrate and create sound, just like a guitar string, but it will not vibrate back and forth around a straight shape. It will vibrate back and forth around its drooping-arch equilibrium state. Gravity does affect the equilibrium state of the wire. But since sound is created by the wire vibrating around its equilibrium state, gravity does not affect the wire's ability to create sound (aside from the fact that it may contribute a little bit of tension to a heavy wire).
Note that, strictly speaking, there is plenty of gravity on a space station in orbit. The astronauts on a space station float around because they are in a continual state of free-fall along with the space station, and not because there is no gravity. You could call this a lack of apparent gravity. In any case, neither true gravity nor apparent gravity have any effect on a guitar string's ability to create sound. Something that does have an effect is air. Sound can only travel from the strings and body of the guitar to a human's ears if there is some air along the way for the sound to travel through. In the vacuum of space, there is effectively zero air. For this reason, sound cannot travel through space. In other words, if an astronaut leaves his air-filled space station and takes his guitar out into space on a spacewalk, another astronaut will not be able to hear the guitar as he plays is. The guitar strings will still vibrate just fine when plucked. But there is no air to transmit the sound from the strings and guitar body to the ears of the other astronauts. The astronaut who is playing the guitar will be able to hear it, since the vibrations can travel directly from the guitar body through his body to his ears without ever needing to go through the air. But to everyone else, a guitar plucked in open space produces no sound. Again, this has nothing to do with a lack of gravity, but is a result of the lack of air.