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?

Question

Arun · Answer

The resonant frequencies of a string are F base 1 = 90 Hz, f base 2 = 150 Hz, f base 3 = 120 Hz a) The highest possible fundamental frequency of the string is f = 30 Hz [because f base 1, f base 2 and f base 3 are integral multiple of 30 Hz] b) The frequencies are f base 1 = 3f, f base 2 = 5f, f base 3 = 7f So, f base 1, f base 2 and f base 3 are 3^rd harmonic, 5^th harmonic and 7th harmonic respectively c) The frequencies in the string are f, 2f, 3f, 4f, 5f, ………. So, 3f = 2^nd overtone and 3^rd harmonic 5f = 4^th overtone and 5^th harmonic 7f = 6^th overtone and 7^th harmonic d) length of the string is l = 80 cm ⇒ f base 1 = (3/2l)v (v = velocity of the wave) ⇒ 90 = {3/(2*80)} * K ⇒ K = (90 * 2 * 80) / 3 = 4800 cm/s = 48 m

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