Find the frequencies of the first three harmonics of a piano string of length 1.5m, if the velocity of the wave on the string is 120ms-1
A. 40Hz, 80Hz, 120Hz B. 80Hz, 160Hz, 240Hz C. 180Hz, 360Hz, 540Hz D. 369Hz, 180Hz, 90Hz
Correct Answer: A
Explanation
in vibrations in string, the fundamental frequency happens to be the first harmonic, and is given as f0 = V/2l. Where V = Velocity of the sound wave, I = Length of the string. The second harmonic is the first overtone given by f1 = V/l = 2f0 ; and the third harmonic happens to be the second overtone, given by f2 = 3V/2l = 2f0. Thus if V = 120m/s and l = 1.5m Thus f1 = 2f0 = 2 x 40 = 80Hz Thus f2 = 3f0 = 3 x 40 = 120Hz Thus we have in order, 40Hz, 80Hz, 120Hz
