The frequency of sound produced by a bell is 500 Hz the velocity of the source relative to still air is 60 m/s. An observer moves at 30 m/s along the same line as the source. Calculate the frequency of sound wave measured by the observer. Consider all possible cases (speed of sound `v=340(m)/(s)`.)

Explanation

CASE I. Let the be at right of the source. Both source and observer are moving in right direction. There will be apparent increase in frequency because `V_("source")gtV_("observer")`
`f'=f_0[(V_S-V_("observer"))/(V_S-V_("source"))]Hz=500[(340-30)/(340-60)]Hz=553Hz`
CASE II. Source is moving right and observer is moving left.
There will be apparent increase in frequency since both are moving towards each other.
`f'=f_0[(V_S+V_("observer"))/(V_S-V_("source"))]Hz=500[(340+30)/(340-60)]Hz`
CASE III. Both source and observer are receding from each other.
There will be an apparent decrease in frequency.
`f'=f_0[(V_S-V_("observer"))/(V_S-V_("source"))]Hz=500[(340-30)/(340+60)]Hz=387.5Hz`
CASE IV. Both source and observer are moving towards left.
`f'=f_0[(V_S+V_("observer"))/(V_S+V_("source"))]=500[(340+30)/(340+60)]Hz=462.5Hz`
You should repeat the example assuming that the observer is to the left of the source. What conclusions can be derived from this example? Do you get a different set of four apparent frequencies.