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A source of sound S emitting ware of frequency $400 \mathrm{HZ}$ and an observer O are located at some distance from each other. The source is moving With a speed of $25 \mathrm{~m} / \mathrm{s}$ at an angle of $30^{\circ}$ with the source observer line as shown in the figure. The observer is at rest. The apparent frequency observed by the observer (velocity of sound in air $332 \mathrm{~m} / \mathrm{s}$ ).

Option: 1
$324Hz$

Option: 2
$428Hz$

Option: 3
$234Hz$

Option: 4
$124Hz$

Answers (1)

$n=n^{\prime}\left(\frac{V}{V-VS \cos \theta}\right)\\$

$n=400\left(\frac{332}{332-25 \times \cos 30^{\circ}}\right) \\$

$n=400\left(\frac{332}{332-25 \times \frac{\sqrt{3}}{2}}\right) \\$

$n=400\left(\frac{332}{\frac{664-25 \sqrt{3}}{2}}\right)$

$n=\frac{400 \times 664}{664-25 \sqrt{3}} \\$

$n=\frac{400 \times 664}{664-25 \times 1.732} \\$

$n=\frac{400 \times 664}{664-43.3} \\$

$n=\frac{400 \times 664}{620.7}$

$n=428\mathrm{~Hz}$

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