The lowest note emitted by a stretched string has a frequency of 40Hz. How many overtones are there between 40Hz and 180Hz?
Answer Details
An overtone is a higher frequency harmonic that is an integer multiple of the fundamental frequency of a vibrating system, such as a stretched string. The first overtone is called the first harmonic, the second overtone is called the second harmonic, and so on.
The frequency of the nth harmonic is given by the equation f_n = n * f_1, where f_1 is the fundamental frequency and n is an integer greater than or equal to 1.
In this case, the fundamental frequency is 40 Hz, so the frequency of the first overtone is 2 * 40 = 80 Hz. The frequency of the second overtone is 3 * 40 = 120 Hz, and the frequency of the third overtone is 4 * 40 = 160 Hz.
Therefore, there are 3 overtones between 40 Hz and 180 Hz, which corresponds to: 3.