Question
In the figure shown a source of sound of frequency $$510\,Hz$$ moves with constant velocity $${v_s} = 20\,m/s$$ in the direction shown. The wind is blowing at a constant velocity $${v_w} = 20\,m/s$$ towards an observer who is at rest at point $$B.$$ Corresponding to the sound emitted by the source at initial position $$A,$$ the frequency detected by the observer is equal to (speed of sound relative to air $$= 330\,m/s$$ )
In the figure shown a source of sound of frequency $$510\,Hz$$ moves with constant velocity $${v_s} = 20\,m/s$$ in the direction shown. The wind is blowing at a constant velocity $${v_w} = 20\,m/s$$ towards an observer who is at rest at point $$B.$$ Corresponding to the sound emitted by the source at initial position $$A,$$ the frequency detected by the observer is equal to (speed of sound relative to air $$= 330\,m/s$$ )
A.
$$510\,Hz$$
B.
$$500\,Hz$$
C.
$$525\,Hz$$
D.
$$550\,Hz$$
Answer :
$$525\,Hz$$
Solution :
Apparent frequency
$$\eqalign{ & n' = n\frac{{\left( {u + {v_w}} \right)}}{{\left( {u + {v_w} - {v_s}\cos {{60}^ \circ }} \right)}} \cr & = \frac{{510\left( {330 + 20} \right)}}{{330 + 20 - 20\cos {{60}^ \circ }}} \cr & = 510 \times \frac{{350}}{{340}} = 525\,Hz \cr} $$
Apparent frequency
$$\eqalign{ & n' = n\frac{{\left( {u + {v_w}} \right)}}{{\left( {u + {v_w} - {v_s}\cos {{60}^ \circ }} \right)}} \cr & = \frac{{510\left( {330 + 20} \right)}}{{330 + 20 - 20\cos {{60}^ \circ }}} \cr & = 510 \times \frac{{350}}{{340}} = 525\,Hz \cr} $$