$A$ vibration magnetometer is used at two different places $A$ and $B$ on the earth. The time period of a magnet suspended freely in the magnetometer at $A$ is twice that at $B$. If the horizontal component of the earth's magnetic field at $B$ is $32 \times 10^{-6} \,T$, then its value at $A$ is

• A
  $H_{A}=8 \times 10^{-6} \,T$
• B
  $H_{A}=32 \times 10^{-6} \,T$
• C
  $H_{A}=4 \times 10^{-6} \,T$
• D
  $H_{A}=16 \times 10^{-6} \,T$