Answer :
Final answer:
To alter a guitar string's fundamental frequency from 124 Hz to 186 Hz, the length of the string must be decreased. The new length is calculated using the ratio of the original to the desired frequency, resulting in the string being pressed at approximately 60 cm from the bridge to achieve a frequency of 186 Hz.
Explanation:
To find where a guitar string should be pressed to alter its fundamental frequency from 124 Hz to 186 Hz, we use the properties of the string and the relationship between frequency, wavelength, and string length. The frequency of a string fixed at both ends is inversely proportional to its length, which means that to increase the frequency, you must reduce the length.
Solving for the desired length involves setting up a ratio of the original and desired frequencies. Since the string's original length is 90 cm and it produces a fundamental frequency of 124 Hz, when the frequency is raised to 186 Hz, the new length (Lnew) can be found using the equation:
Lnew = Loriginal × (foriginal / fnew)
Plugging in the values we get:
Lnew = 90 cm × (124 Hz / 186 Hz)
After calculating, the new length Lnew to produce a fundamental frequency of 186 Hz is approximately 60 centimeters. Thus, the guitarist would need to press the string at the position that shortens its vibrating length to 60 cm from the bridge to achieve the desired frequency.
