Question

A car moves at a speed of $20m{s}^{-1}$ sounding its horn at $480Hz$. If the speed of sound is $340m{s}^{-1}$, the frequency of the reflected sound heard by the girl sitting in the car will be closest to

• A. $540Hz$
• B. $524Hz$
• C. $568Hz$
• D. $480Hz$

Answer 1

The correct option is A

$540Hz$

Step 1. Given data

Frequency of the horn, $f$$=480Hz$

Speed of the car, $v_s=20m{s}^{-}$

Speed of the sound,$v=340m{s}^{-1}$

Step 2. Finding the Apparent frequency before reflection

By using the formula of Apparent frequency, $f^{\text{'}}$

$f^{\text{'}}=\left(\frac{v}{v-v_s}\right)\times f$

$f^{\text{'}}=\left(\frac{340}{340-20}\right)\times 480$

$f^{\text{'}}=510Hz$

Step 3. Finding the Apparent frequency after reflection

After reflection, the girl sitting in the car act as an observer

Apparent frequency after reflection, $f^{\text{'}\text{'}}$

$f^{\text{'}\text{'}}=\left(\frac{v+v_o}{v}\right)\times f^{\text{'}}$

$f^{\text{'}\text{'}}=\left(\frac{340+20}{340}\right)\times 510$

$f^{\text{'}\text{'}}=540Hz$

Therefore, the frequency of the reflected horn heard by girl is $540Hz$

Hence, the correct option is A.