Answer
a. $\lambda=800 km$.
b. Africa-Antarctica, $10.2^{\circ}$. Australia-Antarctica, $12.5^{\circ}$.
Work Step by Step
a. The time between crests is the period, T=1.0 h. The frequency is the reciprocal, so $f=1/T=1.0 h^{-1}$.
Now find the wavelength.
$$\lambda=\frac{v}{f}=\frac{800 km/h}{1.0 h^{-1}}=800 km$$
b. The cancellation points are located at angles that satisfy
$sin \theta=\frac{m \lambda}{a}$, where $m=\pm 1, \pm 2…$.
Africa-Antarctica: find the smallest angle.
$sin \theta_1=\frac{\lambda}{a}$
$$\theta_1 = sin^{-1}(\frac{800km}{4500km})=10.2^{\circ}$$
Australia-Antarctica: find the smallest angle.
$sin \theta_1=\frac{\lambda}{a}$
$$\theta_1 = sin^{-1}(\frac{800km}{3700km})=12.5^{\circ}$$
