Question

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

• A. 24%
• B. 6%
• C. 12%
• D. 18%

Answer 1

The correct option is C 12%

$n_{max}=\left(\frac{V-V_0}{V-V_s}\right)n(\because V_0=0)$
$n_{max}=\left(\frac{V}{V-V_s}\right)n;n_{max}=\left(\frac{320}{320-20}\right)\times 1000$
$=1066\text{Hz}$
$n_{min}=\left(\frac{V}{V+V_s}\right)n=\frac{320}{320+20}\times 1000=941\text{Hz}$
$\Delta n=1066-941=125$
$\frac{\Delta n}{n}\times 100=\frac{125}{1000}\times 100=12.5\%$