## College Physics (4th Edition)

(a) The observed frequency is $3.0~kHz$ (b) The observed frequency is $333.3~Hz$ (c) The observed frequency is $1.0~kHz$
(a) We can use the equation for the Doppler effect when the source and observer are moving toward each other: $f_o = \left(\frac{v+v_o}{v-v_s}\right)~f_s$ $f_o = \left(\frac{v+v/2}{v-v/2}\right)~f_s$ $f_o = \left(\frac{3v/2}{v/2}\right)~f_s$ $f_o = 3~f_s$ $f_o = (3)~(1.0~kHz)$ $f_o = 3.0~kHz$ The observed frequency is $3.0~kHz$ (b) We can use the equation for the Doppler effect when the source and observer are moving away from each other: $f_o = \left(\frac{v-v_o}{v+v_s}\right)~f_s$ $f_o = \left(\frac{v-v/2}{v+v/2}\right)~f_s$ $f_o = \left(\frac{v/2}{3v/2}\right)~f_s$ $f_o = \left(\frac{1}{3}\right)~f_s$ $f_o = \left(\frac{1}{3}\right)~(1000~Hz)$ $f_o = 333.3~Hz$ The observed frequency is $333.3~Hz$ (c) We can use the equation for the Doppler effect when the source and observer are moving in the same direction: $f_o = \left(\frac{v-v_o}{v-v_s}\right)~f_s$ $f_o = \left(\frac{v-v/2}{v-v/2}\right)~f_s$ $f_o = f_s$ $f_o = 1.0~kHz$ The observed frequency is $1.0~kHz$.