A) D. 285Hz
We can solve the problem by using the Doppler effect formula:
[tex]f'=(\frac{v-v_o}{v-v_s})f[/tex]
where
f' is the apparent frequency
v = 340 m/s is the velocity of the sound wave
[tex]v_o = -5.0 m/s[/tex] is the velocity of the observer (the cyclist, in this case), which is negative because the cyclist is moving towards the sound source
[tex]v_s = 0[/tex] is the velocity of the sound source (zero, in this case, since the musician is stationary)
f = 281 Hz is the original frequency
Substituting into the equation, we find:
[tex]f'=(\frac{340 m/s-(-5.0 m/s)}{340 m/s-0})(281 Hz)=285 Hz[/tex]
B) B. 277 Hz
Similarly, we can solve the problem by using the Doppler effect formula:
[tex]f'=(\frac{v-v_o}{v-v_s})f[/tex]
where
f' is the apparent frequency
v = 340 m/s is the velocity of the sound wave
[tex]v_o = +5.0 m/s[/tex] is the velocity of the observer (the cyclist, in this case), which is now positive because the cyclist is moving away from the sound source
[tex]v_s = 0[/tex] is the velocity of the sound source (zero, in this case, since the musician is stationary)
f = 281 Hz is the original frequency
Substituting into the equation, we find:
[tex]f'=(\frac{340 m/s-(+5.0 m/s)}{340 m/s-0})(281 Hz)=277 Hz[/tex]
