Two men are walking along a horizontal straight line in the same direction. The man in front walks at a speed 1.0   m   s - 1 and the man behind walks at a speed 2.0   m   s - 1 . A third man is standing at a height 12   m above the same horizontal line such that all three…

Question

Two men are walking along a horizontal straight line in the same direction. The man in front walks at a speed 1.0 &#160; m &#160; s - 1 and the man behind walks at a speed 2.0 &#160; m &#160; s - 1 . A third man is standing at a height 12 &#160; m above the same horizontal line such that all three men are in a vertical plane. The two walking men are blowing identical whistles which emit a sound of frequency 1430 &#160; H z . The speed of sound in air is 330 &#160; m &#160; s - 1 . At the instant, when the moving men are 10 &#160; m apart, the stationary man is equidistant from them. The frequency of beats in H z , heard by the stationary man at this instant, is __________.

Aicharya · Accepted Answer

cos ⁡ θ = 5 13 f A = 1430 330 330 - 2 cos ⁡ θ = 1430 1 1 - 2 cos ⁡ θ 330 = 1430 1 + 2 cos ⁡ θ 330 (By binomial expansion) f B = 1430 330 330 + 1 cos ⁡ θ = 1430 1 - cos ⁡ θ 330 ∆ f = f A - f B = 1430 3 cos ⁡ θ 330 = 13 cos ⁡ θ = 13 5 13 = 5.00 H z

Two men are walking along a horizontal straight line in the same direction. The man in front walks at a…

Solution