A car moving at 72 km/h finds another car in front of it going in the same direction at 36 km/h. The first…

A car moving at 72 km/h finds another car in front of it going in the same direction at 36 km/h. The first car sounds a horn that has a dominant frequency of 900 Hz. What will be the apparent frequency heard by the driver in the front car? (Take, speed of sound in air = 330 ms -1)

Solution

Sol. The given situation is shown below. $\rightarrow\ v_s\qquad\ \rightarrow\ v_o$ $\bullet\ \ S\qquad\ \ \bullet\ \ O$ $\longrightarrow\ v$ Velocity of source, $v_s = 72\ \text{km/h}$ = $72 \times \frac{5}{18}$ = $20\ \text{m/s}$ Velocity of observer, $v_o = 36\ \text{km/h}$ = $36 \times \frac{5}{18}$ = $10\ \text{m/s}$ $v = 330\ \text{ms}^{-1}$ and $f = 900\ \text{Hz}$ Apparent frequency, $f' = f\left(\frac{v - v_o}{v - v_s}\right)$ = $900\left(\frac{330 - 10}{330 - 20}\right)$ = $929\ \text{Hz}$ Answer: 929 Hz

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