Question 535: Waves

Question

A whistling train approaches a junction. An 
observer standing at the junction observes 
the frequency to be 2.2 kHz and 1.8 kHz 
of the approaching and the receding train. 
Find the speed of the train (speed of sound 
= 300 m/s).

Accepted Answer

Let the speed of the train be V$$_t$$,
Let $$v$$ be the actual frequency of the whistle.
Speed of sound $$\mathrm{V}_{s}=300 \mathrm{~m} / \mathrm{s}$$
While train is approaching, $$v_{2}=2.2 \mathrm{~kHz}$$
$$=2.2	imes10^3$$ Hz
$$v_{2}=\frac{\mathrm{V}_{s}}{\mathrm{~V}_{s}-\mathrm{V}_{t}} 	imes v$$
$$2.2 	imes 10^{3}=\frac{\mathrm{V}_{s}}{\mathrm{~V}_{s}-\mathrm{V}_{t}} 	imes v=\frac{300}{300-\mathrm{V}_{t}} 	imes v$$ ...... (i)
While train is receding,
$$v_1=1.8$$ kHz = $$1.8	imes10^3$$ Hz
$${v_1} = {{{V_s}} \over {{V_s} + {V_t}}} 	imes v$$
$$1.8 	imes {10^3} = {{300} \over {300 + {V_t}}} 	imes v$$ .... (ii)
Dividing equation (i) by (ii)
$${{2.2 	imes {{10}^3}} \over {1.8 	imes {{10}^3}}} = {{{{300} \over {300 - {V_t}}} 	imes v} \over {{{300} \over {300 + {V_t}}} 	imes v}}$$
$$ = {{2.2} \over {1.8}} = {{300 + {V_t}} \over {300 - {V_t}}}$$
$$660 - 2.2\,{V_t} = 540 + 1.8\,{V_t}$$
$$2.2\,{V_t} + 1.8\,{V_t} = 660 - 540$$
$$4{V_t} = 120$$
$${V_t} = 30$$ m/s

Answer

30

Answer

20

Answer

60

Answer

75

Waves

A whistling train approaches a junction. An observer standing at the junction observes the frequency to be 2.2 kHz and 1.8 kHz of the approaching and the receding train. Find the speed of the train (speed of sound = 300 m/s).

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