Answer:
Part a)
f = 1112.3 Hz
Part b)
L = 94.2 dB
Explanation:
Part a)
As we know by Doppler's Effect of sound that when source of sound and observer moves relative to each other then the frequency of sound observed by the observer is different from actual frequency
Here when source and observer is moving towards each other then the observed frequency is given by
[tex]f = f_o\frac{v + v_0}{v- v_s}[/tex]
now plug in all values in it
[tex]f = 965 (\frac{343 + 15.7}{343 - 31.8})[/tex]
[tex]f = 1112.3 Hz[/tex]
Part b)
Power of the siren is given as
[tex]P = 45.2 W[/tex]
Now the intensity of sound received by driver of car is given as
[tex]I = \frac{P}{4\pi r^2}[/tex]
[tex]I = \frac{45.2}{4\pi (36.8)^2}[/tex]
[tex]I = 2.66 \times 10^{-3} W/m^2[/tex]
now the decibel level of sound is determined by
[tex]L = 10 Log \frac{I}{I_o}[/tex]
now we have
[tex]L = 10 Log\frac{2.66 \times 10^{-3}}{10^{-12}}[/tex]
[tex]L = 94.2 dB[/tex]