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jelliott

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Blog Entries posted by jelliott

  2. jelliott
    They said senior year would be a breeze. To avoid such a horrifying prospect, I decided to indulge in AP-C Physics, which, as they say, is one of the most challenging classes the school has to offer. But, as the Chinese proverb goes, "The gem cannot be polished without friction, nor man perfected without trials".

    I am not taking AP-C Physics simply because I enjoy torturing myself with hard problems. In actuality, I hope to be able to tackle hard problems step-by-step. There is always a logical process to everything, and that idea alone is why science exists. So, knowing this, I hope to increase my arsenal of processes this year.

    AP-B Physics was my most challenging class thus far, but also my most interesting one. The idea that this sometimes chaotic world can operate in such mathematical order is still pretty incredible to me, and I took this class to further understand the relationships that exist in the world around us. It's quite nifty.

    I'm definitely nervous to solve more complex problems than I ever have before, using calculus. Calculus is still some obscure, evil concept to me. And on that note, I'm excited to be able to utilize it and learn something that I will hopefully use throughout college and beyond. To quote another proverb here: "Just when the caterpillar thought the world was over...it became a butterfly", and I look forward to becoming a beautiful physics butterfly this year.
  3. jelliott
    My last one, I promise.

    When I stumbled upon Mr. Grimes' paper regarding all of these guitar applications to physics, I had already known that things like harmonics had to do with basic string/wave physics - but all of these other applications have really interested me, as someone who loves the instrument. If you're interested at all, visit the source material; he obviously worked very hard on it, and his hard work shines through.

    http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0102088

    This final post focuses on yet another vital guitar technique that is prevalent in so many solos - Hendrix and Van Halen were masters at it, and Stevie Ray Vaughan's subtle uses of the tremolo bar added so much character to his already impressive blues playing.

    The whammy bar in a typical Fender Stratocaster fits directly into the bridge as shown above, and by applying a torque to the whammy bar, the bridge experiences a slight rotational acceleration in order to change the frequencies of the strings. As we know, a force exerted closer to the bridge would provide less torque, and thus, less rotation. However, apply that same force near the bend in the bar (close to the white tip), and your torque is significantly greater. (Net torque equals force times length.)

    Well, the new frequency provided by a whammy bar can be determined from this equation derived by Grimes:

    This is a manipulation of his previous equation, determining frequency of a stretched string.

    The whammy bar equation is essentially identical, except in the numerator of that radical fraction, the force applied to the whammy bar (F subscript W) is added to the tension of the string. The plus and minus indicates that the whammy bar can go both ways, although on the typical Stratocaster, it is much harder to pull up on the bar and raise the pitch than it is to depress it and lower the pitch.

    If you don't have a locked-in bridge, though, you're not likely to use this tool as frequently - otherwise, the forces applied onto the bridge alter the tensions of the strings, in other words making them very out of tune. For those using a Strat, remember to whammy in short bursts and with much smaller rotational forces, so that you don't have to stop to tune in the middle of a song.

    Citation:
    Grimes, David R. "String Theory - The Physics of String-Bending and Other Electric Guitar Techniques." PLOS ONE:. N.p., 23 July 2014. Web. 23 Nov. 2014.
  4. jelliott
    I made a post a while back about the physics behind pinch harmonics - but, since there is a multitude of other guitar techniques, there's a lot more physics to be explored with this instrument.

    Think about your all-time favorite guitar solo, and I'll guarantee you that there is bending somewhere in it. It's the technique that must be mastered to make a decent solo, and it's in all of the best ones: it's ever-present in legendary solos such as Pink Floyd's "Comfortably Numb", Lynyrd Skynyrd's "Freebird", and Eagles' "Hotel California", just to scratch the surface.

    Surprisingly, there's a whole bunch of complicated equations to describe the nature of bending, relating the bend angle theta to a change in frequency. An impressive and detailed paper was written about all of these techniques by David Robert Grimes, an Oxford scientist who obviously has a passion for this stuff. I'll be referencing his findings throughout these posts.

    First of all, the fundamental frequency for a bent string can be described by where l is string length, T is its tension, and u is its linear mass density. With the application of an extending force, its bend frequency can be given in terms of the bend angle. Theta is the bend angle, and F subscript E is the perpendicular force exerted on the fretboard. Note that this equation only holds up when assuming that the increase in string length caused by bending is negligible.

    But as we have learned, the magnitude of the restoring force of an elastic object is given by F = kx, Hooke's Law, where k is the elastic constant and x is the displacement. This can be rearranged using Young's modulus (E), which depends on material, and the string's cross-sectional area (A). kx and EA both represent the stiffness of the string. Therefore, we can replace F subscript E with known variables, and with some simplification, end up with an equation for the frequency of the bent string:

    Some side notes are that 1. Young's Modulus, a measurement of stiffness, vary due to string material. 2. The area also varies from string to string - some guitarists prefer thicker strings than others. 3. According to Grimes, the typical bend angle does not exceed 1.5 degrees.

    Next time, we'll look at vibrato, which, excitingly enough, involves derivatives. Woohoo.

    Citation:
    Grimes, David R. "String Theory - The Physics of String-Bending and Other Electric Guitar Techniques." PLOS ONE:. N.p., 23 July 2014. Web. 23 Nov. 2014.
  5. jelliott

    Orbital Decay and You

    By jelliott,

    (You, of course, indicating its impact on the Earth and not necessarily you on a personal level.)

    By essentially sapping energy from an orbital system, gravitational radiation makes orbits more circular and continuously decreases their radii. Overall angular momentum decreases, as this too is essentially stolen by radiation. The decrease in the radius of orbit is given by the following equation:

    Substitution of the Earth's and Sun's masses for m1 and m2 tells us that the rate of our orbit with the Sun is decreasing by the second: 1.1 * 10^-20 meters per second, to be exact. Not to freak you out or anything, but we're getting closer and closer to the Sun as you read this. In exactly 365 days (that's a year in math terms), we will be MUCH closer to the Sun than we are now. About 1/300 of the diameter of a hydrogen atom. Now that's a bafflingly huge number, but I'm sure we have a few years left under our belt before we collapse into the Sun and die fiery deaths.

    This equation can tell us the lifetime of an orbit as well, before this collapsing occurs. However, since the rate of change depends on the radius and not time, integration of the equation is necessary. So the lifetime of an orbital radius is brought to you by this guy here:

    Again, substituting in the Earth's and Sun's masses, we find our orbit to be about 1.09 * 10^23 years. Seems pretty massive, especially considering this is 10^13 times larger than the age of the Universe itself.

    Well, I hope you learned something, and I'll see you next quarter.

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