the apparent frequency of a note when listenermoves towards a stationary source with velocity 40m/s is 200Hzwhen he moves from the same source with same speed the apparent frequency of note is 160Hz. calculate velocity of sound in air

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Solution

$f i r s t c a s e a p p a r e n t f r e q u e n c y i s g i v e n b y : r ν' = \frac{v + v_{l}}{v} ν_{0} w h e ν v i s t h e v e l o c i t ν y o f s u n d i n a i r v_{l} i s t h e v e l o c i t y o f l i s t n e r ν_{0} = i n i t i a l f r e q u e n c y 200 = \frac{v + 40}{v} ν_{0} - - - - - (1) f o r s e c o n d c a s e : ν' = \frac{v - v_{l}}{v} ν_{0} 160 = \frac{v - 40}{v} ν_{0} - - - - (2) d i v i d e t h e s e t w o e q u a t i o n s, w e g e t v = 360 m / s$

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the apparent frequency of a note when listenermoves towards a stationary source with velocity 40m/s is 200Hzwhen he moves from the same source with same speed the apparent frequency of note is 160Hz. calculate velocity of sound in air

first case apparent frequency is given by:rν' = v+vlvν0wheν v is the velocitνy of sund in airvl is the velocity of listnerν0 = initial frequency200 = v+40vν0-----(1)for second case:ν' = v-vlvν0160 = v-40vν0----(2)divide these two equations, we get v = 360 m/s