A source of sound S emitting waves of frequency $$100$$ Hz and an observer O are located at some distance from each other. The source is moving with a speed of $$19.4$$ $$ms-1$$ at an angle of $$60$$° 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 $$330$$ $$ms-1$$, is

Question

A source of sound S emitting waves of frequency $$100$$ Hz and an observer O are located at some distance from each other. The source is moving with a speed of $$19.4$$ $$ms-1$$ at an angle of $$60$$° 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 $$330$$ $$ms-1$$, is

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Here, Frequency of source, $$v0=100$$ Hz Velocity of source, $$vs=19.4$$ $$ms-1$$ Velocity of sound in air, $$v=330$$ $$ms-1As$$ the velocity of source along the source observer line is vs $$cos$$ $$60$$° and the observer is at rest, so the apparent frequency observed by the observer $$isv=v0vv-vscos60$$°$$=(100$$ $$Hz)330$$ $$ms-1330$$ $$ms-1-19.4$$ $$ms-112=(100$$ $$Hz)330$$ $$ms-1330$$ $$ms-1-9.7$$ $$ms-1=(100$$ $$Hz)330$$ $$ms-1320.3$$ $$ms-1=103$$ Hz

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