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What is Dopper effect ? Obtainan expression for the apparent frequency of sound heard when the source is in motion with respect to an observer at rest. |
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Answer» Solution :Doppler effect `:` The apparent change in the frequency heard by the observer due to the relative motion between the observer and the SOURCE of sound is calleddopplerd effect. When a whistling railway engine APPROACHES an observer standing on the platform, the frequency of sound appears to increase. When it moves away the frequency appear to decrease.  Expression for apparent frequency when source is in motion and listener at rest `:` Let S = Source of sound O = Listener Let 'S' be the source, moving with a velocity `'upsilon_(s)'` to wards the stationary listener. The distance TRAVELLED by the source in time period `'T' = upsilon _(s). T ` Thereforethe successive compressions and rarefactions are drawn closer to listener. `:. ` Apparent wavelength ` lambda' = lambda - upsilon_(s) T `. `lambda' = lambda- ( upsilon_(s))/(v) [ :' v = (1)/(T)]` `= ( lambdav =- upsilon_(s))/( v)= (upsilon-upsilon_(s))/(v)``[ :' v = v lambda ]` If" v' " is apparent frequency heard by the listener. then `v'= (upsilon)/( lambda')`where `'upsilon'` is velocity of sound in air. `v' = (upsilon.v )/( upsilon-v_(s))` Therefore the apparent frequency is greater than the actual frequency . Similary , if the sourceis away from the stationary listener thenapparent frequency`v' = ( upsilon.v)/( upsilon+ upsilon_(s))` , which is less than the actual frequency. LIMITATION `:` Doppler effectis applicable when the VELOCITIES of the source and listener are much less than that of sound velocity. |
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