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14. waves and sound — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics14. waves and sound1 Mark
MCQ
A bus driving along at $39.6 \,km / h$ is approaching a person who is standing at the bus stop, while honking repeatedly at an interval of $30 \,s$. If the speed of sound is $330 \,ms ^{-1}$, at what interval will the person hear the horn?
  • A
    $31 \,s$
  • ✓
    $29 \,s$
  • C
    $30 \,s$
  • D
    The interval will depend on the distance of the bus from the passenger
✓

Answer

Correct option: B.
$29 \,s$
b
(b)

Here, source is moving towards a stationary observer.

Given,

Velocity of source, $v_s=39.6 \,km / h$

$=39.6 \times \frac{5}{18}=11 \,ms ^{-1}$

Velocity of sound, $v=330 \,ms ^{-1}$

Frequency of source, $f=\frac{1}{30} \,s ^{-1}$

So, apparent frequency of sound as heard by the observer is

$f^{\prime}=\left(\frac{v}{v-v_s}\right) \cdot f=\left(\frac{330}{330-11}\right) \cdot \frac{1}{30}$

$\Rightarrow \quad f^{\prime}=\frac{11}{319}$

$\Rightarrow \quad f^{\prime}=\frac{1}{29}$

So, time interval between two honks of bus horn observed by observer (person at bus stop) is $29 \,s$.

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