A string of length 0.860m is stretched tightly between fixed ends. The string is plucked and vibration is created that travels with a speed of 125m/s along the string.
a) determine the fundamental frequency and the frequencies of the first two overtones.
b) Are the overtones harmonics of the fundamental frequency? (check if the overtones are whole multiples of the fundamental frequency.)
oh and can someone also explain to me what is fundamental frequency and overtones? Thanks
The fundamental frequency is given by
speed = frequency x wavelength
We know the length of the wave must be 0.860m, and the speed is 125m/s.
125 = 0.860 F
125/0.860 = F
F = 145Hz
The fundamental, or natural frequency, is the frequency in which the wavelength is the longest; the longest possible wavelength here is .86m, so 145Hz is the fundamental.
Overtones and harmonics are two terms for very similar things. Overtones are usually used in music, while harmonics are used in physics. Both refer to variations in a wave.
The actual definition of an overtone is any frequency higher than the fundamental, but in music it normally refers to integer multiples of that frequency. This is the same thing as a harmonic; integer multiples of the frequency. However, they are counted differently; the first harmonic is the fundamental. The first overtone is the first integer multiple of the fundamental (i.e., 2 x the fundamental).
If 145Hz is the fundamental, it is also the first harmonic.
2 x 145 = 290Hz, the second harmonic, and the first overtone.
3 x 145 = 435Hz, the third harmonic, and the second overtone.