Question

Three resonant frequencies of a string are 90, 150 and 210 Hz.

(a) Find the highest possible fundamental frequency of vibration of this string.

(b) Which harmonics of the fundamental are the given frequencies ?

(c) Which overtones are these frequencies.

(d) If the length of the string is 80 cm, what would be the speed of a transverse wave on this string ?

Answer 1

The resonant frequencies of a string are
f1 = 90 Hz, f2 = 150 Hz, f3 = 120 Hz
a) The highest possible fundamental frequency of the string is f = 30 Hz
[because f1, f2 and f3 are integral multiple of 30 Hz]
b) The frequencies are f1 = 3f, f2 = 5f, f3 = 7f
So, f1, f2 and f3 are 3rd harmonic, 5th harmonic and 7th harmonic respectively.
c) The frequencies in the string are f, 2f, 3f, 4f, 5f, ……….