As we increase the mass per unit length of the string, frequency goes down (think of the larger strings on a piano that are responsible for the lower frequencies). We call this a 5th. To further your understanding of these relationships and the use of the above problem-solving scheme, examine the following problem and its solution. Keeping mass per unit length and tension constant, how much shorter would you have to make the string? A guitar string has a number of frequencies at which it will naturally vibrate. The length of a guitar string is related mathematically to the wavelength of the wave which resonates within it. A pitch of Middle D (first harmonic = 294 Hz) is sounded out by a vibrating guitar string. -Now what about if you quadrupled the tension T? The most common used in music today is (from biggest string to smallest): E, A, D, G, B, E. If your computer has a microphone, you can use the tuner below. The major 7th is widely considered smooth and comforting. To get the necessary mass for the strings of an electric bass as shown above, wire is wound around a solid core wire. Answers: f1 = 250 Hz; f2 = 500 Hz; f3 = 750 Hz. For the first harmonic, the wavelength is twice the length. Turns out this value is what mostly determines the tone that you hear.
Now that the wavelength is found, the length of the guitar string can be calculated. Calculate the frequency of the first, second, and third harmonics. If the length of a guitar string is known, the wavelength associated with each of the harmonic frequencies can be found. By how much would the tension have to be reduced? I wouldn't suggest actually trying that on your guitar, but could you lower the frequency by an octave (half of the original frequency) by reducing the tension? Avoid the tendency to memorize approaches to different types of problems.