A car $'A'$ chasing another car $'B'$ with a speed of $20\, m/s$ sounding a horn of $180\, Hz$. While both cars are moving towards a stationary siren of frequency $170\, Hz$. What is the speed of car $B$ so that it can't hear any beat ....$m/s$ (speed of sound $= 340\, m/s$)
Diffcult
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Car $B$ hear freq. from stationary siren
${\mathrm{n}_{1}=\mathrm{n}\left(\frac{\mathrm{V}+\mathrm{V}_{0}}{\mathrm{V}}\right)} $
${\mathrm{n}_{1}=170\left(\frac{340+\mathrm{V}}{340}\right)}$
Car $B$ hear freq. from Car $A$
$\mathrm{n}_{2}=\mathrm{n}\left(\frac{\mathrm{V}-\mathrm{V}_{0}}{\mathrm{V}-\mathrm{V}_{\mathrm{s}}}\right)$
$\mathrm{n}_{2}=180\left(\frac{340-\mathrm{V}_{0}}{340-20}\right)=180\left(\frac{340-\mathrm{V}}{320}\right)$
for no beats
$\mathrm{n}_{1}=\mathrm{n}_{2}$
$170\left(\frac{340+\mathrm{V}}{340}\right)=180\left(\frac{340-\mathrm{V}}{320}\right)$
$\mathrm{V}=20 \mathrm{\,m} / \mathrm{s}$
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