Question

The amplitude of a transverse wave on a string is 3.0 cm. The ratio of the maximum particle speed to the speed of the wave is 3.9. What is the wavelength (in cm) of the wave?

Answer 1

Therefore the wavelength of the particle is 4.83 m.

Step-by-step 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
`C_(max)`= A×ω

The speed of the particle C= f×λ

Then,

`(C_max)/(C) =(A* \omega)/(f* \lambda)`

`\Rightarrow (C_max)/(C) =(A* 2\pi * f)/(f* \lambda)` [∵ω=2πf]

`\Rightarrow (C_max)/(C) =(A* 2\pi )/( \lambda)`

`\Rightarrow 3.9=(3* 2\pi )/( \lambda)`

`\Rightarrow \lambda=(3* 2\pi )/( 3.9)`

`\Rightarrow \lambda = 4.83` m

Therefore the wavelength of the particle is 4.83 m