$A$ transverse sinusoidal wave of amplitude '$a$',wavelength $\lambda$,and frequency $f$ is travelling on a stretched string. The maximum speed at any point on the string is $v/10$,where $v$ is the speed of propagation of the wave. If $a = 10^{-3} \ m$ and $v = 10 \ ms^{-1}$,then $\lambda$ and $f$ are given by:

• A
  $\lambda = 2\pi \times 10^{-2} \ m, f = \frac{10^3}{2\pi} \ Hz$
• B
  $\lambda = 10^{-2} \ m, f = 10^3 \ Hz$
• C
  $\lambda = 10^{-3} \ m, f = 10^4 \ Hz$
• D
  $\lambda = \frac{10^{-2}}{2\pi} \ m, f = 2\pi \times 10^{-2} \ Hz$