Answer
(a) The frequency of the sound received by a stationary observer is $2.0~kHz$
(b) The frequency of the sound received by a stationary observer is $666.7~Hz$
Work Step by Step
(a) We can find the speed of the source:
$v_s = (0.50)~(343~m/s) = 171.5~m/s$
We can use the equation for the Doppler effect when the source is approaching:
$f_o = \left(\frac{v}{v-v_s}\right)~f_s$
$f_o = \left(\frac{343~m/s}{343~m/s-171.5~m/s}\right)~(1.0~kHz)$
$f_o = 2.0~kHz$
The frequency of the sound received by a stationary observer is $2.0~kHz$
(b) We can use the equation for the Doppler effect when the source is moving away:
$f_o = \left(\frac{v}{v+v_s}\right)~f_s$
$f_o = \left(\frac{343~m/s}{343~m/s+171.5~m/s}\right)~(1000~Hz)$
$f_o = 666.7~Hz$
The frequency of the sound received by a stationary observer is $666.7~Hz$
