Answer:
-3.396 m/s or 3.465 m/s
Explanation:
v = Speed of sound in air = 343 m/s
[tex]v_s[/tex] = Relative speed of the singer
f = Observed frequency
f' = Actual frequency
1% change can mean [tex]f=1.01f'[/tex]
From the Doppler effect equation we have
[tex]f=f'\dfrac{v}{v+v_s}\\\Rightarrow 1.01f'=f'\dfrac{v}{v+v_s}\\\Rightarrow 1.01=\dfrac{343}{343+v_s}\\\Rightarrow v_s=\dfrac{343}{1.01}-343\\\Rightarrow v_s=-3.396\ m/s[/tex]
The velocity is -3.396 m/s
when [tex]f=0.99f'[/tex]
[tex]f=f'\dfrac{v}{v+v_s}\\\Rightarrow 0.99f'=f'\dfrac{v}{v+v_s}\\\Rightarrow 0.99=\dfrac{343}{343+v_s}\\\Rightarrow v_s=\dfrac{343}{0.99}-343\\\Rightarrow v_s=3.46464646465\ m/s[/tex]
The velocity is 3.465 m/s
