Subjective Type

In Fig. $$ 35-38, $$ sources $$ A $$ and $$ B $$ emit long-range radio waves of wavelength $$ 400 \mathrm{m}, $$ with the phase of the emission from $$ A $$ ahead of that from source $$ B $$ by $$ 90^{\circ} . $$ The distance $$ r_{A} $$ from $$ A $$ to detector $$ D $$ is greater than the corresponding distance $$ r_{B} $$ by $$ 100 \mathrm{m} . $$ What is the phase difference of the waves at $$ D ? $$

Solution

Initially, source $$ A $$ leads source $$ B $$ by $$ 90^{\circ}, $$ which is equivalent to $$ 1 / 4 $$ wavelength.
However, source $$ A $$ also lags behind source $$ B $$ since $$ r_{A} $$ is longer than $$ r_{B} $$ by $$ 100 \mathrm{m} $$, which is $$ 100 \mathrm{m} / 400 \mathrm{m}=1 / 4 $$ wavelength.
So the net phase difference between $$ A $$ and $$ B $$ at the detector is zero.

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