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Dua dawai baja sejenis memberikan nada dasar . Jik...

Dua dawai baja sejenis memberikan nada dasar begin mathsize 14px style 200 space Hz end style. Jika panjang salah satu dawai ditambah begin mathsize 14px style 5 percent sign end style, berapakah frekuensi layangan yang terjadi?

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Jawaban:

Diketahui :
begin mathsize 14px style f subscript 0 equals 200 space H z L subscript 0 equals L L apostrophe equals L subscript 0 plus 0 comma 05 L subscript 0 equals 1 comma 05 L subscript 0 equals 1 comma 05 L end style

Ditanya :
begin mathsize 14px style f subscript l a y a n g a n end subscript equals.... ? end style

Penyelesaian :

Langkah 1 : Menghitung Besarnya begin mathsize 14px style f apostrophe end style

Berdasarkan persamaan,

 begin mathsize 14px style f subscript n equals fraction numerator n plus 1 over denominator 2 L end fraction v end style

Maka kita mendapatkan hubungan antara frekuensi dengan panjang dawai, yakni :

begin mathsize 14px style f tilde 1 over L end style

Maka,

begin mathsize 14px style thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space fraction numerator f subscript 0 over denominator f apostrophe end fraction equals fraction numerator L apostrophe over denominator L subscript 0 end fraction fraction numerator 200 space Hz over denominator f apostrophe end fraction equals fraction numerator 1 comma 05 L over denominator L end fraction thin space thin space 200 space Hz equals 1 comma 05 cross times f apostrophe thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space f apostrophe equals fraction numerator 200 space Hz over denominator 1 comma 05 end fraction thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space f apostrophe equals 190 comma 5 space Hz end style

Langkah 2 : Menghitung begin mathsize 14px style f subscript l a y a n g a n end subscript end style 

begin mathsize 14px style f subscript l a y a n g a n end subscript equals open vertical bar f apostrophe minus f subscript 0 close vertical bar thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space equals open vertical bar 190 comma 5 space Hz space minus space 200 space Hz close vertical bar thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space thin space equals 9 comma 5 space Hz end style


Jadi, frekuensi layangan yang terjadi sebesar 9,5 Hz.

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