A source of sound S emitting waves of frequency and an observer O are located at some distance from each other. The source is moving with a speed of at an angle of with the source-observer line as shown in the figure. The observer is at rest. The apparent frequency observed by the observer (velocity of sound in air ), is:
According to the Doppler effect, the apparent frequency heard by a stationary observer when the source is moving at an angle to the line joining them is given by considering the component of the source's velocity along the line of sight. The component of the velocity of the source approaching the observer is . The formula for apparent frequency when the source approaches a stationary observer is: where is the velocity of sound, is the velocity of the source, and is the actual frequency. Substituting the given values: Thus, the apparent frequency observed is approximately .
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