$$v = f\lambda$$
Where:
- v is the wave speed in meters per second (m/s)
- f is the frequency of the wave in hertz (Hz)
- λ is the wavelength of the wave in meters (m)
In this case, the fundamental frequency of the string is given as 220 Hz, and the length of the string is 75 m. The wavelength of the fundamental mode of a vibrating string is twice the length of the string, so:
$$\lambda = 2L = 2(75\text{ m}) = 150\text{ m}$$
Substituting the values of f and λ into the formula, we get:
$$v = f\lambda = (220\text{ Hz})(150\text{ m}) = 33000\text{ m/s}$$
Therefore, the wave speed along the vibrating string is 33,000 m/s.