Answer
(a) increase
(b) stay the same (but increase relative to rest)
(c) stay the same (but decrease relative to rest)
(d) stay the same
Work Step by Step
(a) We know that $I=\frac{P}{2\pi r^2}$. This equation shows that $r$ is inversely proportional to the intensity of the sound. When the train moves towards the observer $r$ will decrease and as a result the intensity of the sound will increase.
(b) As $f^{\prime}=(\frac{v}{v-u_s})f$. This equation shows that the velocity of train $u_s$ is less than the velocity of sound $v$, hence the denominator of equation(2) is less than the numerator that is $f^{\prime}\gt f$ and thus the observed frequency will increase relative to the train being at rest. However, as the train moves closer to the observer, the frequency will not change.
(c) We know that $f^{\prime}=\frac{v}{\lambda^{\prime}}$. This equation shows that the frequency is inversely proportional to the wavelength. Thus, when the frequency increases then the observed wavelength will decrease relative to the train being at rest. However, as the train moves closer to the observer, the wavelength will not change.
(d) We know that $v=\sqrt{\frac{K_s}{\rho}}$. This equation shows that velocity of the sound depends on the properties of the medium; hence the velocity of sound will remain constant and will not increase or decrease as the train gets closer.
