Doppler

Question

A speeding motorcyclist sees traffic jam ahead him. He slows down to 36 km hour${}^{-1}$. He finds that traffic has eased and a car moving ahead of him at 18 km hour${}^{-1}$ is honking at a frequency of 1392 Hz. If the speed of sound is 343 m${s}^{-1}$, the frequency of the honk as heard by him will be

Easy

Solution

Here speed of Motorcyclist speed is

${v}_{m}=36\mathrm{km}{\text{hour}}^{-1}=36\times \frac{5}{18}\mathrm{m}{\mathrm{s}}^{-1}=10\mathrm{m}{\mathrm{s}}^{-1}$

Speed of car,

${v}_{c}=18\mathrm{km}{\text{hour}}^{-1}=18\times \frac{5}{18}\mathrm{m}{\mathrm{s}}^{-1}=5\mathrm{m}{\mathrm{s}}^{-1}$

Frequency of source, ${\nu}_{0}$= 1392 Hz

Speed of sound, $\nu =$343 m ${s}^{-1}$

The frequency of the honk heard by the motorcyclist is

${v}^{\text{'}}={v}_{0}\left(\frac{v+{v}_{m}}{v+{v}_{c}}\right)=1392\left(\frac{343+10}{343+5}\right)=\frac{1392\times 353}{348}=1412\mathrm{Hz}$

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