Question

A transverse wave is represented by the equation

Answer 1

Explanation:

Wave velocity is vv.

Particle velocity is

\dfrac {dy}{dt} = y_{0}\cos \dfrac {2\pi}{\lambda} (vt - x) \dfrac {2\pi}{\lambda} v

dt

dy

=y

0

cos

λ

2π

(vt−x)

λ

2π

v

\left (\dfrac {dy}{dt}\right )_{max} = y_{0}\dfrac {2\pi v}{\lambda}(

dt

dy

)

max

=y

0

λ

2πv

But, maximum particle velocity is 2 times the wave velocity.

\dfrac{2\pi v}{\lambda}y_o = 2v

λ

2πv

y

o

=2v

\therefore \lambda = \pi y_{0}∴λ= πy

0