To solve this problem it is necessary to apply the concepts related to wavelength depending on the frequency and speed. Mathematically, the wavelength can be expressed as
[tex]\lambda = \frac{v}{f}[/tex]
Where,
v = Velocity
f = Frequency,
Our values are given as
L = 3.6m
v= 192m/s
f= 320Hz
Replacing we have that
[tex]\lambda = \frac{192}{320}[/tex]
[tex]\lambda = 0.6m[/tex]
The total number of 'wavelengths' that will be in the string will be subject to the total length over the size of each of these undulations, that is,
[tex]N = \frac{L}{\lambda}[/tex]
[tex]N = \frac{3.6}{0.6}[/tex]
[tex]N = 6[/tex]
Therefore the number of wavelengths of the wave fit on the string is 6.
