Answer :
Final answer:
To produce a fundamental frequency of 186 Hz, the guitar string should be pressed at a distance of 60 cm from the end of the string.
Explanation:
To produce a fundamental frequency of 186 Hz, the guitar string should be pressed at a distance of 60 cm from the end of the string.
One way to solve this problem is to use the formula for the speed of a wave on a string:
speed = frequency x wavelength
In this case, the speed of the wave remains constant, so we can use the formula:
speed = frequency1 x wavelength1 = frequency2 x wavelength2
Since the length of the string is given as 90 m, we can calculate the wavelength of the fundamental frequency (124 Hz) using the formula:
wavelength1 = length/number of nodes
wavelength1 = 90 m / 2 = 45 m
Substituting the values into the wave equation:
frequency1 x wavelength1 = frequency2 x wavelength2
124 Hz x 45 m = 186 Hz x ?m
After solving for the unknown wavelength, we find that ?m = 30 cm.
