(a) 1440.5 Hz
The general formula for the Doppler effect is
[tex]f'=(\frac{v+v_r}{v+v_s})f[/tex]
where
f is the original frequency
f is the apparent frequency
[tex]v[/tex] is the velocity of the wave
[tex]v_r[/tex] is the velocity of the receiver (positive if the receiver is moving towards the source, negative otherwise)
[tex]v_s[/tex] is the velocity of the source (positive if the source is moving away from the receiver, negative otherwise)
Here we have
f = 1110 Hz
v = 334 m/s
In the reflector frame (= on surface B), we have also
[tex]v_s = v_A = -28.7 m/s[/tex] (surface A is the source, which is moving towards the receiver)
[tex]v_r = +62.2 m/s[/tex] (surface B is the receiver, which is moving towards the source)
So, the frequency observed in the reflector frame is
[tex]f'=(\frac{334 m/s+62.2 m/s}{334 m/s-28.7 m/s})1110 Hz=1440.5 Hz[/tex]
(b) 0.232 m
The wavelength of a wave is given by
[tex]\lambda=\frac{v}{f}[/tex]
where
v is the speed of the wave
f is the frequency
In the reflector frame,
f = 1440.5 Hz
So the wavelength is
[tex]\lambda=\frac{334 m/s}{1440.5 Hz}=0.232 m[/tex]
(c) 1481.2 Hz
Again, we can use the same formula
[tex]f'=(\frac{v+v_r}{v+v_s})f[/tex]
In the source frame (= on surface A), we have
[tex]v_s = v_B = -62.2 m/s[/tex] (surface B is now the source, since it reflects the wave, and it is moving towards the receiver)
[tex]v_r = +28.7 m/s[/tex] (surface A is now the receiver, which is moving towards the source)
So, the frequency observed in the source frame is
[tex]f'=(\frac{334 m/s+28.7 m/s}{334 m/s-62.2 m/s})1110 Hz=1481.2 Hz[/tex]
(d) 0.225 m
The wavelength of the wave is given by
[tex]\lambda=\frac{v}{f}[/tex]
where in this case we have
v = 334 m/s
f = 1481.2 Hz is the apparent in the source frame
So the wavelength is
[tex]\lambda=\frac{334 m/s}{1481.2 Hz}=0.225 m[/tex]
