Question

If a guitar string has a fundamental frequency of 500 Hz, which one of the following frequencies can set the string into resonant vibration?

a. 250 Hz
b. 1500 Hz
c. 1750 Hz
d. 750 Hz

Answer 1

The frequency that can set the string into resonant vibration is 1,500 Hz.

Step-by-step explanation:

Given;

fundamental frequency of the string, F₀ = 500 Hz

The frequencies that can set the string into resonant vibration must be higher frequencies, such frequencies include the first overtone, second overtone, third overtone, etc.

The first overtone, F₁ = 2F₀ = 2 x 500 = 1,000 Hz

The second overtone, F₂ = 3F₀ = 3 x 500 = 1,500 Hz

The third overtone, F₃ = 4F₀ = 4 x 500 = 2,000 Hz

Therefore, the frequency that can set the string into resonant vibration is 1,500 Hz.