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An airplane is in supersonic flight at an altitude h. At what smallest distance a (along the horizontal) from the observer on the ground is there a point from which the sound emitted by the airplane motors travels to the observer faster than from point A that is directly above the observer – (a) a (b) a (c) not possible for any real value of a (d) a>2(v_p/v_s )/((v_p/v_s )^2-1) h where vp = velocity of airplane, vs = velocity of sound

An airplane is in supersonic flight at an altitude h. At what smallest distance a (along the horizontal) from the observer on the ground is there a point from which the sound emitted by the airplane motors travels to the observer faster than from point A that is directly above the observer –
 
    (a)    a<2(v_p/v_s )/((v_p/v_s )^2-1) h
    (b)    a<((v_p/v_s ))/((v_p/v_s )^2-1) h
    (c)    not possible for any real value of a
    (d)    a>2(v_p/v_s )/((v_p/v_s )^2-1) h
    where vp = velocity of airplane, vs = velocity of sound


Grade:upto college level

1 Answers

Radhika Batra
247 Points
7 years ago

(a)

    t = √(a^2+h^2 )/v_s  =>  t_2=a/v_p +h/v_s ;    t1 < t2¬

    a < 2(v_p/v_s )/((v_p/v_s )^2-1) h

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