wavelength) and knowledge of the speed and frequency to determine the wavelength.However, the frequency and speed are given, so one can use the wave equation (speed = frequency From the graphic above, the only means of finding the length of the string is from knowledge of the wavelength. The problem statement asks us to determine the length of the guitar string.

The speed of waves in a particular guitar string is known to be 405 m/s. To further your understanding of these relationships and the use of the above problem-solving scheme, examine the following problem and its solution.Įxample Problem #2 Determine the length of guitar string required to produce a fundamental frequency (1st harmonic) of 256 Hz. Avoid the tendency to memorize approaches to different types of problems. It is important to combine good problem-solving skills (part of which involves the discipline to set the problem up) with a solid grasp of the relationships among variables. The tendency to treat every problem the same way is perhaps one of the quickest paths to failure. Seldom in physics are two problems identical. These preparatory steps become more important as problems become more difficult. It is always wise to take the extra time needed to set the problem up take the time to write down the given information and the requested information and to draw a meaningful diagram. Most problems can be solved in a similar manner. Now that wavelength is known, it can be combined with the given value of the speed to calculate the frequency of the first harmonic for this given string. This relationship, which works only for the first harmonic of a guitar string, is used to calculate the wavelength for this standing wave. This relationship is derived from the diagram of the standing wave pattern (and was explained in detail in Lesson 4 ). For the first harmonic, the wavelength is twice the length. In this problem (and any problem), knowledge of the length and the harmonic number allows one to determine the wavelength of the wave. If the wavelength could be found, then the frequency could be easily calculated. The speed is given, but wavelength is not known.

wavelength) and knowledge of the speed and wavelength.

From the graphic above, the only means of finding the frequency is to use the wave equation (speed=frequency The problem statement asks us to determine the frequency (f) value. The solution to the problem begins by first identifying known information, listing the desired quantity, and constructing a diagram of the situation. Determine the fundamental frequency (1st harmonic) of the string if its length is 76.5 cm. To demonstrate the use of the above problem-solving scheme, consider the following problem and its detailed solution.Įxample Problem #1 The speed of waves in a particular guitar string is 425 m/s. These relationships will be used to assist in the solution to problems involving standing waves in musical instruments. The graphic below depicts the relationships between the key variables in such calculations. Each of these calculations requires knowledge of the speed of a wave in a string. And conversely, calculations can be performed to predict the natural frequencies produced by a known length of string. Thus, the length-wavelength relationships and the wave equation (speed = frequency * wavelength) can be combined to perform calculations predicting the length of string required to produce a given natural frequency. If the length of a guitar string is known, the wavelength associated with each of the harmonic frequencies can be found.

The wavelength of the standing wave for any given harmonic is related to the length of the string (and vice versa). The graphic below depicts the standing wave patterns for the lowest three harmonics or frequencies of a guitar string. For now, we will merely summarize the results of that discussion. The specifics of the patterns and their formation were discussed in Lesson 4. Each of these natural frequencies or harmonics is associated with a standing wave pattern. As mentioned earlier, the natural frequency at which an object vibrates at depends upon the tension of the string, the linear density of the string and the length of the string. These natural frequencies are known as the harmonics of the guitar string. A guitar string has a number of frequencies at which it will naturally vibrate.

Guitar string notes