Answer:
The first harmonic is: 250Hz, second harmonic 500Hz, third harmonic 750Hz.
Explanation:
Use the frequency f, speed v, and wavelentgh L relationship:
[tex]v = f\cdot L\implies f = \frac{v}{L}[/tex]
We are given the speed v=400 m/s. The base wavelength on a string of length 80cm is twice the length of the string (a "half wave" along the full length of the string), so:
[tex]f = \frac{400\frac{m}{s}}{2\cdot0.8 m}= 250\frac{1}{s}=250 Hz[/tex]
The fundamental frequency (first harmonic) is 250 Hz
The second harmonic is produced by one full wave across the string (adding one node in the middle), so L=80cm in this case, therefore the second harmonic frequency is: f2 = 2*250=500Hz
the third harmonic add another node (and a half wave) to the pattern and the wavelength will be 2/3 of 80cm, so f3=3*250Hz = 750Hz
