It looks like you're working on a problem related to waves. The problem gives the amplitude of a transverse wave on a string as 6.48 cm and states that the ratio of the maximum particle speed to the speed of the wave is 3.51. You need to determine the wavelength of the wave.

Here's how we can approach the problem:

1. Amplitude and particle speed: The amplitude is the maximum displacement from the equilibrium position, which is 6.48 cm. The ratio of the maximum particle speed (which is related to the speed of the wave) to the speed of the wave is 3.51.

2. Relationship between wave speed, particle speed, and amplitude: The maximum particle speed $v_{\text{particle}}$ for a transverse wave is related to the wave speed $v_{\text{wave}}$ and the amplitude $A$ by the equation:

   $v_{\text{particle}} = A \cdot \omega$ where $\omega$ is the angular frequency, which is related to the wave speed and the wavelength by the formula:

   $\omega = \frac{2 \pi v_{\text{wave}}}{\lambda}$ where $\lambda$ is the wavelength.

3. Solving for the wavelength: The ratio of maximum particle speed to wave speed is given by:

   $\frac{v_{\text{particle}}}{v_{\text{wave}}} = 3.51$

   Using the equation for particle speed, you can substitute and solve for the wavelength $\lambda$.

Would you like me to solve the equation step-by-step?