![]() 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.
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