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Giải bài 6.60 trang 23 sách bài tập toán 11 - Kết nối tri thức với cuộc sống

Cent âm nhạc là một đơn vị trong thang lôgarit của cao độ hoặc khoảng tương đối.

Tổng hợp đ𝓀ề thi học kì 2 lớp 11 tất cả các môn - Kết nối tri thức

Toán - Văn - Anh - Lí - Hóa - Sinh
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Đề bài

Cent âm nhạc là một đơn vị trong thang lôgarit của cao độ hoặc khoảng tương đối. Một quãng tám bằng 1200 cent. Công thức xác định chênh lệch khoảng thời gian (tính bằng cent) giữa hai nốt nhạc có tần số a và \(b\) là \(n = 1200 \cdot {\rm{lo}}{{\rm{g}}_2}\frac{a}{b}{\rm{\;}}{\rm{.}}\)

(Theo Algebra 2, NXB MacGraw-Hill, 2008)

a) Tìm khoảng thời gian tính bằng cent khi tần số thay đổi từ \(443{\rm{\;Hz}}\) về \(415{\rm{\;Hz}}\). b) Giả sử khoảng thời gian là 55 cent và tần số đầu là \(225{\rm{\;Hz}}\), hãy tìm tần số cuối cùng.

Phương pháp giải - Xem chi tiết

a) Tính \(n = 1200 \cdot {\rm{lo}}{{\rm{g}}_2}\frac{a}{b}{\rm{\;}}\) khi \(a = 443{\rm{\;Hz}}\) và \(b = 415{\rm{\;Hz}}\) b) Giải phương trình \(55 = 1200 \cdot {\rm{lo}}{{\rm{g}}_2}\frac{{225}}{b}\), ta được \(b\).

Lời giải chi tiết

a) Khoảng thời gian giữa hai nốt nhạc khi tần số thay đổi từ \(443{\rm{\;Hz}}\) về \(415{\rm{\;Hz}}\)là \(1200 \cdot {\rm{lo}}{{\rm{g}}_2}\frac{{443}}{{415}} \approx 113\) (cent).b) Giải phương trình \(55 = 1200 \cdot {\rm{lo}}{{\rm{g}}_2}\frac{{225}}{b}\), ta được \(b \approx 218\).Vậy tần số cuối cùng cần tìm là \(218{\rm{\;Hz}}\).
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