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------------------------------------------------ A guitar string is 90 cm long and has a fundamental frequency of 124 Hz. To produce a fundamental frequency of 186 Hz, the guitar should be pressed at:

A. 60 cm
B. 30 cm
C. 20 cm
D. 10 cm

Question

High School

Answer :

akash71 akash71 · Answer 1 · 2023-11-02T02:31:11-04:00

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.

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.