Answer:
Therefore the wavelength of the particle is 4.83 m.
Explanation:
Transverse wave: A transverse wave is a moving wave whose direction of wave and oscillation are perpendicular to each other.
Amplitude:The amplitude of a wave is the maximum the distance from its rest position covered by a particle.
Here amplitude (A) = 3.0 cm
The ratio of maximum speed to the speed of the particle is 3.9
The maximum speed of the particle [tex]C_{max}[/tex]= A×ω
The speed of the particle C= f×λ
Then,
[tex]\frac{C_max}{C} =\frac{A\times \omega}{f\times \lambda}[/tex]
[tex]\Rightarrow \frac{C_max}{C} =\frac{A\times 2\pi \times f}{f\times \lambda}[/tex] [∵ω=2πf]
[tex]\Rightarrow \frac{C_max}{C} =\frac{A\times 2\pi }{ \lambda}[/tex]
[tex]\Rightarrow 3.9=\frac{3\times 2\pi }{ \lambda}[/tex]
[tex]\Rightarrow \lambda=\frac{3\times 2\pi }{ 3.9}[/tex]
[tex]\Rightarrow \lambda = 4.83[/tex] m
Therefore the wavelength of the particle is 4.83 m
