Answer: a) 16Hz, 3m b) 48Hz, 1mc) 80Hz, 0.6m
Explanation:
a) Fundamental frequency in string is represented as Fo = V/2L where;
Fo is the fundamental frequency
V is the speed of the transverse wave = 48m/s
L is the length of the wire. = 1.50m
Substituting this values in the formula given we have;
Fo = 48/2(1.5)
Fo = 48/3
Fo = 16Hz
The fundamental tone is therefore 16Hz
Using v =f¶
Where f is the frequency and ¶ is the wavelength, the wavelength of the fundamental note will be;
¶ = v/fo
¶ = 48/16 = 3m
b) Overtones or harmonics is the multiple integral of the fundamental frequency. The multiples are I'm arithmetical progression.
First overtone f1 = 2fo
Second overtone f2 = 3fo etc.
Since fo = 16Hz
Second overtone f2 = 3×16 = 48Hz
¶ = v/f2 = 48/48
¶ = 1m
c) Fourth harmonic or overtone will be f4 = 5fo
F4 = 5×16 = 80Hz
The fourth harmonic is therefore 80Hz
¶ = v/f4 = 48/80
¶ = 0.6m
