A man is watching two trains, one leaving and the other coming in with equal speeds of $$4$$ $$m/$$$$sec$$. If they sound their whistles, each of frequency $$240$$ Hz, the number of beats heard by the man (velocity$$ of sound in air $$=$$ $$320$$ $$m/$$$$sec$$$$) will be equal to

Question

A man is watching two trains, one leaving and the other coming in with equal speeds  of $$4$$ $$m/$$$$sec$$. If they sound their whistles, each of frequency $$240$$ Hz, the number of beats heard by the man (velocity$$ of sound in air $$=$$ $$320$$ $$m/$$$$sec$$$$) will be equal to

Infinity Learn · Accepted Answer

Frequency of sound heard by the man from approaching $$trainna=n$$ vv−$$vs=240$$ $$320320$$−$$4=243$$ Hz  Frequency of sound heard by the man from receding train $$nr=n$$ $$vv+vs=240$$ $$320320+4=237HzHence$$, number of beats heard by man per $$sec$$   $$=na$$−$$nr=243$$−$$237=6Short$$ trick : Number of beats heard per $$sec$$   $$=2nvvSv2$$−$$vS2=2nvvS(v$$−$$vS)(v+vS)=2$$×$$240$$×$$320$$×$$4(320$$−$$4)(320+4)=6$$

A man is watching two trains, one leaving and the other coming in with equal speeds of 4 m/sec. If they sound their whistles, each of frequency 240 Hz, the number of beats heard by the man (velocity of sound in air = 320 m/sec) will be equal to

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