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
-
40Hz, 80Hz, 120Hz
- 80Hz, 160Hz, 240Hz
- 180Hz, 360Hz, 540Hz
- 369Hz, 180Hz, 90Hz
The correct answer is: A
Explanation
in vibrations in string, the fundamental frequency happens to be the first harmonic, and is given as
f\(_0\) = \(\frac{V}{2l}\)
Where V = Velocity of the sound wave, I = Length of the string.
The second harmonic is the first overtone given by
f1 = \(\frac{V}{l}\) = 2f0 ;
and the third harmonic happens to be the second overtone, given by
f2 = \(\frac{3V}{2l}\) = 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
There is an explanation video available .