Answer:
The ratio is 9.95
Solution:
As per the question:
Amplitude, [tex]y_{m} = 8.4\ cm[/tex]
Wavelength, [tex]\lambda = 5.3\ cm[/tex]
Now,
To calculate the ratio of the maximum particle speed to the speed of the wave:
For the maximum speed of the particle:
[tex]v_{m} = y_{m}\times \omega[/tex]
where
[tex]\omega = 2\pi f[/tex] = angular speed of the particle
Thus
[tex]v_{m} = 2\pi fy_{m}[/tex]
Now,
The wave speed is given by:
[tex]v = f\lambda[/tex]
Now,
The ratio is given by:
[tex]\frac{v_{m}}{v} = \frac{2\pi fy_{m}}{f\lambda}[/tex]
[tex]\frac{v_{m}}{v} = \frac{2\pi \times 8.4}{5.3} = 9.95[/tex]
