91Ó°ÊÓ

$f_L=\left(\frac{v+v_L}{v+v_s}\right)f_s$where ${\mathrm{f}}_{\mathrm{L}}$is the observer frequency of sound, v is the speed of sound waves,$V_{\mathrm{S}}$is observer velocity, localid="1664336719942" ${\mathrm{V}}_{\mathrm{L}}$is source velocity and ${\mathrm{f}}_{\mathrm{s}}$is actual frequency of sound waves.

${\mathrm{f}}_{\mathrm{s}}=1000\mathrm{Hz}$, The positive direction is from the listener to the source $\mathrm{v}=344\mathrm{m}/\mathrm{s}$.

(a)

$$\begin{gathered} \mathrm{v}=\left(344\mathrm{m}/\mathrm{s}\right)/2 \\ =-172\mathrm{m}/\mathrm{s} \\ {\mathrm{v}}_{\mathrm{L}}=0\mathrm{m}/\mathrm{s} \end{gathered}$$

Apply in doppler’s equation,

$$\begin{gathered} {\mathrm{f}}_{\mathrm{L}}=\left(\frac{\mathrm{v}+{\mathrm{v}}_{\mathrm{L}}}{\mathrm{v}+{\mathrm{v}}_{\mathrm{s}}}\right){\mathrm{f}}_{\mathrm{s}} \\ =\left(\frac{344\mathrm{m}/\mathrm{s}}{344\mathrm{m}/\mathrm{s}-172\mathrm{m}/\mathrm{s}}\right)\left(1000\mathrm{Hz}\right) \\ =2000\mathrm{Hz} \end{gathered}$$

Hence, when the source moves towards the listener the frequency heard by him would be 2000Hz.

(b) ${\mathrm{v}}_{\mathrm{s}}=0,{\mathrm{v}}_{\mathrm{L}}=172\mathrm{m}/\mathrm{s}$

$$\begin{gathered} {\mathrm{f}}_{\mathrm{L}}=\left(\frac{\mathrm{v}+{\mathrm{v}}_{\mathrm{L}}}{\mathrm{v}+{\mathrm{v}}_{\mathrm{s}}}\right){\mathrm{f}}_{\mathrm{s}} \\ =\left(\frac{344\mathrm{m}/\mathrm{s}+172\mathrm{m}/\mathrm{s}}{344\mathrm{m}/\mathrm{s}}\right)\left(1000\mathrm{Hz}\right) \\ =1500\mathrm{Hz} \end{gathered}$$

Hence, when the listener moves towards the source the frequency heard by him would be 1500Hz.

The answer in (b) is much less than the answer in (a). It is the velocity of the source and listener relative to the air that determines the effect, not the relative velocity of the source and listener relative to each other.