Question

A locomotive approaching a crossing at a speed of \[20{\text{m/s}}\], If a whistle of frequency \[640{\text{Hz}}\] when \[1{\text{km}}\], there is no need and the speed of sound in air is \[330{\text{m/s}}\]. What frequency is heard by an observer \[\sqrt 3 {\text{km}}\] of the straight road from the crossing at a right angle.
\[
  {\text{A}}{\text{. 600 Hz}} \\
  {\text{B}}{\text{. 630Hz}} \\
  {\text{C}}{\text{. 660Hz}} \\
  {\text{D}}{\text{. 720Hz}} \\
 \]

Answer 1

Hint: Doppler effect can basically be said to be a property of sound wave. We will discuss their effect in the article and also learn about the Doppler effect formula and application after the calculation the Doppler effect various situations without any base. The change in the sound wave frequency because of movement is referred to as the Doppler effect which is also referred to as the Doppler shift. For instance imagine you are standing on the pavement and a police car speed past you.

Complete answer:
Velocity in direction observe from source,
\[ Vcos \theta \] = \[20 \times \dfrac{1}{2}{\text{ }} \to {\text{V = 10m/s}}\]
By Doppler effect-
\[{\text{N = u}} \ne {\text{ }}\dfrac{{\text{V}}}{{({\text{V - }}{{\text{v}}^ \circ })}}\]
\[\mu \]= \[640 \times \dfrac{{330}}{{(330 - 10)}}\]
\[\mu \] = \[640 \times \dfrac{{330}}{{320}}\]
\[\mu \] = \[660 Hz\]

Hence, option C is the correct option.

Additional information:
The sound is heard by the listener if the source of that sound and the listener are moving relative to each other. This is what the Doppler effect is when the listener and the source move close, the frequency which the listener hears is higher than the sound which the source emits.
Similarly, when the listener and the source move away from one another, the frequency which the listener hears is lower than the frequency which the listener hear it lower than the frequency of the sound from the source. The unit of sound frequency is Hertz (Hz). Over one hertz is a cycle per second. \[\left( {1{\text{Hz = }}\dfrac{1}{{s - 1}} = 1{\text{ cycle/s}}} \right)\]

Note:
Use a proper formula that does not forget to write the unit of the answer. Always write the last answer with the final statement. Hence by using the Doppler effect formula we have the frequency of the sound.