Answer
(a) The observed frequency is $1.5~kHz$
(b) The observed frequency is $500~Hz$
Work Step by Step
(a) We can use the equation for the Doppler effect when the observer is approaching:
$f_o = \left(\frac{v+v_o}{v}\right)~f_s$
$f_o = \left(\frac{v+v/2}{v}\right)~f_s$
$f_o = \left(\frac{3}{2}\right)~f_s$
$f_o = \left(\frac{3}{2}\right)~(1.0~kHZ)$
$f_o = 1.5~kHz$
The observed frequency is $1.5~kHz$
(b) We can use the equation for the Doppler effect when the observer is moving away:
$f_o = \left(\frac{v-v_o}{v}\right)~f_s$
$f_o = \left(\frac{v-v/2}{v}\right)~f_s$
$f_o = \left(\frac{1}{2}\right)~f_s$
$f_o = \left(\frac{1}{2}\right)~(1000~Hz)$
$f_o = 500~Hz$
The observed frequency is $500~Hz$
