A supersonic jet plane moves parallel to the ground at speed v = 0.75 mach (1 mach = speed of sound). The frequency of its engine sound is $v_o=2kHz$ and the height of the jet plane is h = 1.5 km. At some instant an observer on the ground hears a sound of frequency $v=2_o$. Find the instant (in sec) prior to the instant of hearing when the sound wave received by the observer was emitted by the jet plane. Velocity of sound wave in the condition of observer = 340 m/s. 

Doppler's effect formula is used to determine the frequency of the sound heard by the observer when there is relative motion between the observer and the sound source. The motion formula is used to determine how long it takes to travel a distance at a constant speed.

The apparent frequency of the sound observed by the observer is less or greater than the actual frequency when there is relative motion between the source of the sound and the observer, depending on the direction of the motion of the source of the sound.

The apparent frequency perceived will be lower than the sound's actual frequency if the source of the sound is moving away from the observer.
The apparent frequency observed will be higher than the original frequency of the sound if the source of the sound is traveling in the direction of the observer.
Using the Doppler effect equation,

$f_{app}=f_o\left(\frac{v_{\text{sound }}-v_{\text{observer }}}{v_{\text{sound }}-v_{\text{source }}}\right)$
Given that the observer is at rest and that the perceived frequency is double the sound's original frequency, this statement is true.
$2f_o=f_o\left(\frac{v_{\text{sound }}-0}{v_{\text{sound }}-v_{\text{jet }}\cos \theta }\right)$
Here, $\theta$is the angle created between the horizontal and the jet's direction.
$\Rightarrow 2=\left(\frac{v_{\text{sound }}}{v_{\text{sound }}-0.75v_{\text{sound }}\cos \theta }\right)$
$\Rightarrow 2=\frac{1}{1-0.75\cos \theta }$
$\Rightarrow 2-1.5\cos \theta =1$
$\Rightarrow 1.5\cos \theta =1$
$\Rightarrow \cos \theta =\frac{1}{1.5}$
$\Rightarrow \cos \theta =\frac{2}{3}$

Trigonometric identity is used to

$\sin \theta =\sqrt{1-{\cos }^2\theta }$
$=\sqrt{1-{\left(\frac{2}{3}\right)}^2}$
$=\sqrt{1-\frac{4}{9}}$
$\sin \theta =\frac{\sqrt{5}}{3}$
the length of the jet's flight in a direction perpendicular to the horizontaltaken travel$=d=\frac{h}{\sin \theta }$$d=\frac{1500}{\left(\frac{\sqrt{5}}{3}\right)}m=2012.5m$
Time is taken travele by the sound $t=\frac{\text{ dis }\tan ce}{\text{ speed }}=\frac{2012.5}{340}\approx 6\sec$

Hence, the correct answer is option D.