Question

A train is moving on a straight track with speed $20{ms}^{-1}$. It is blowing its whistle at the frequency of $1000Hz$. The percentage change in the frequency heard by a person standing near the track as the train passes him is (speed of sound = $320{ms}^{-1}$) close to

• A. 12%
• B. 18%
• C. 24%
• D. 60%

Answer 1

The correct option is A 12%

$f_1$ (train approaches)

$f_1=v_0\left(\frac{v}{v-v_s}\right)$

$=1000\left(\frac{320}{320-20}\right)=1000\left(\frac{320}{300}\right)Hz.$

$f_2$ (train recedes)

$f_2=v_0\left(\frac{v}{v+v_s}\right)$

$=1000\left(\frac{320}{320+20}\right)=1000\left(\frac{320}{340}\right)Hz.$

$△f=\left(\frac{f_1-f_2}{f_1}\right)\times 100$
$=11.7$% $\approx 12$ %