A bus moving with an uniform speed of $72 \mathrm{~km} / \mathrm{h}$ towards a building blows a horn of frequency $1.7 \mathrm{kHz}$. If speed of sound in air is $340 \mathrm{~m} / \mathrm{s}$, what will be the frequency of echo heard by bus driver?

• Correct answer
  A

  $1.8 \mathrm{kHz}$
• B

  $2.0 \mathrm{kHz}$
• C

  $1.6 \mathrm{kHz}$
• D

  $1.4 \mathrm{kHz}$

Solution

According to Doppler's effect, Observed frequency of sound reflected from building is given by
Here, $v=$ speed of sound $=340 \mathrm{~m} / \mathrm{s}$, $v_b=$ speed of bus $=7.2 \mathrm{~km} / \mathrm{h}=20 \mathrm{~ms}^{-1}$ and $f=$ original frequency produced by horn $=1.7 \mathrm{kHz}$ Hence, putting these value in Eq. (i), we get Observed frequency by bus driver, $f^{\prime}=1.7\left(\frac{340+20}{340-20}\right)=1.9125 \mathrm{kHz} \approx 1.8 \mathrm{kHz}$

Hence, the correct answer is option: 'A'.