Observational detection of quasi-periodic drifting fine structures in a type III radio burst associated with a solar flare SOL2015-04-16T11:22, with Low Frequency Array, is presented. Although similar modulations of the type III emission have been observed before and were associated with the plasma density fluctuations, the origin of those fluctuations was unknown. Analysis of the striae of the intensity variation in the dynamic spectrum allowed us to reveal two quasi-oscillatory components. The shorter component has the apparent wavelength of $sim2$ Mm, phase speed of $sim657$ km s$^{-1}$, which gives the oscillation period of $sim3$ s, and the relative amplitude of $sim0.35$%. The longer component has the wavelength of $sim12$ Mm, and relative amplitude of $sim5.1$%. The short frequency range of the detection does not allow us to estimate its phase speed. However, the properties of the shorter oscillatory component allowed us to interpret it as a fast magnetoacoustic wave guided by a plasma non-uniformity along the magnetic field outwards from the Sun. The assumption that the intensity of the radio emission is proportional to the amount of plasma in the emitting volume allowed us to show that the superposition of the plasma density modulation by a fast wave and a longer-wavelength oscillation of an unspecified nature could readily reproduce the fine structure of the observed dynamic spectrum. The observed parameters of the fast wave give the absolute value of the magnetic field in the emitting plasma of $sim1.1$ G which is consistent with the radial magnetic field model.
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