Statement $-1$ : Due to the motion of listener, the frequency of the sound waves (as received by listener) emitted by stationary source is affected.
Statement $-2$ : Due to the motion of source, wavelength of the sound waves (emitted by source) as received by stationary listener is affected.
Statement $-3$ : If receiver and source both are moving, the observed frequency must be different from the original frequency of source.
Treat motion of source or listener as always along a line joining them for all above cases.
Medium
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$\mathrm{f}^{\prime}=\left(\frac{\mathrm{V} \pm \mathrm{V}_{0}}{\mathrm{V} \pm \mathrm{V}_{\mathrm{s}}}\right) \mathrm{f}$
$\mathrm{f}_{1}=\left(\frac{\mathrm{V} \pm \mathrm{V}_{0}}{\mathrm{V}}\right) \mathrm{f}$
$\mathrm{f}_{2}=\left(\frac{\mathrm{V}}{\mathrm{V} \pm \mathrm{V}_{\mathrm{S}}}\right) \mathrm{S}$
$\lambda_{2}=\left(\frac{\mathrm{V} \pm \mathrm{V}_{\mathrm{S}}}{\mathrm{f}}\right)$
$\mathrm{V}_{0}=$ velocity of listener, $\mathrm{V}_{\mathrm{s}}=$ Velocity of source
But if ${\overrightarrow {\rm{V}} _{\rm{S}}} = {\overrightarrow {\rm{V}} _0}$ then ${{\rm{f}}^\prime } = {\rm{f}}$
Thus statement - $3$ is not always correct
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