To solve this problem it is necessary to apply the concepts related to wavelength as a function of frequency and speed, as well as to determine the wavelength as a function of length.
From the harmonic vibration generated we know that the total length of the string will be equivalent to a half of the wavelength, that is
[tex]L = \frac{\lambda}{2} \rightarrow \lambda = 2L[/tex]
Where,
[tex]\lambda =[/tex] Wavelength
Therefore the wavelength for us would be,
[tex]\lambda = 2*47.5cm = 95cm = 0.95m[/tex]
From the relationship of speed, frequency and wavelength we know that
[tex]\lambda = \frac{v}{f} \rightarrow v = \lambda f[/tex]
[tex]v = (0.95m)(245Hz)[/tex]
[tex]v = 232.75 m/s[/tex]
Therefore the speed of the wave is 232.75m/s
