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Tentukan frekuensi senar dari bahan yang sama yang panjangnya 2 kali panjang senar tersebut jika tegangan senar diperbesar 3 kali!

Tentukan frekuensi senar dari bahan yang sama yang panjangnya 2 kali panjang senar tersebut jika tegangan senar diperbesar 3 kali!

  1. 80 square root of 3 space Hz

  2. 80 square root of 2 space Hz

  3. 40 square root of 3 space Hz

  4. 40 square root of 2 space Hz

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R. Anjasmara

Master Teacher

Mahasiswa/Alumni Universitas Riau

Jawaban terverifikasi

Pembahasan

Diketahui : Berdasarkan persamaan hukum Mersenne. Maka (frekuensi baru)nya adalah :

Diketahui :

calligraphic l subscript a equals 50 space cm equals 0 comma 5 space straight m

f subscript a equals 160 space H z

calligraphic l subscript straight b equals 2 calligraphic l subscript straight a space

straight rho subscript straight a equals straight rho subscript straight b

straight A subscript straight a equals straight A subscript straight b

straight F subscript straight b equals 3 straight F subscript straight a straight f subscript senar space end subscript ?

Berdasarkan persamaan hukum Mersenne.

straight f subscript straight a equals space fraction numerator 1 over denominator 2 calligraphic l subscript straight a end fraction space square root of fraction numerator straight F subscript straight a over denominator straight rho subscript straight a straight A subscript straight a end fraction end root 160 equals fraction numerator 1 over denominator 2 cross times 0 comma 5 end fraction square root of fraction numerator straight F subscript straight a over denominator straight rho subscript straight a straight A subscript straight a end fraction end root

160 equals square root of fraction numerator straight F subscript straight a over denominator straight rho subscript straight a straight A subscript straight a end fraction end root

Maka straight f subscript straight b (frekuensi baru)nya adalah :

straight f subscript straight b equals space fraction numerator 1 over denominator 2 calligraphic l subscript straight b end fraction space square root of fraction numerator straight F subscript straight b over denominator straight rho subscript straight b straight A subscript straight b end fraction end root

straight f subscript straight b equals space fraction numerator 1 over denominator 2 straight x 2 straight x calligraphic l subscript straight a end fraction space square root of fraction numerator 3 xF subscript straight a over denominator straight rho subscript straight a straight A subscript straight a end fraction end root

straight f subscript straight b equals space fraction numerator 1 over denominator 4 straight x calligraphic l subscript straight a end fraction square root of fraction numerator 3 xF subscript straight a over denominator straight rho subscript straight a straight A subscript straight a end fraction end root

straight f subscript straight b equals space fraction numerator 1 over denominator 4 straight x 0 comma 5 end fraction cross times square root of 3 cross times square root of fraction numerator straight F subscript straight a over denominator straight rho subscript straight a straight A subscript straight a end fraction end root

straight f subscript straight b equals space 1 half cross times square root of 3 cross times 160 equals 80 space square root of 3 space space Hz

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