A sample contains water at two locations, x = 0 cm and x = 2.0 cm. A one-dimensional magnetic field gradient of 1 G/cm is applied along the x-axis during the acquisition of an FID. The frequency encoding gradient is 1 G/cm. What frequencies (relative to the isocenter frequency) are contained in the Fourier transformed spectrum?

The frequency encoding equation is

Δν = γ x G
where:
Δν = frequency offset from isocenter
γ = gyromagnetic ratio, 42.58 MHz/T
G = frequency encoding gradient = 0.0001 T/cm
x = position relative to isocenter

x = 0 cm, Δν = 0

x = 2.0 cm, Δν = 8.516 kHz