SOAL DAN PEMBAHASAN PIPA ORGANA

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بِسْــــــــــــــــمِ اﷲِالرَّحْمَنِ اارَّحِيم

KONSEP DASAR:

ν
f = ^____
λ

Keterangan:
f = frekuensi gelombang (Hz)
ν = cepat rambat gelombang (m/s)
λ = panjang gelombang (m)

Soal No. 1

Baca Juga

Sebuah pipa organa yang terbuka kedua ujungnya memiliki nada dasar dengan frekuensi sebesar 300 Hz. Tentukan besar frekuensi dari :
a) Nada atas pertama
b) Nada atas kedua
c) Nada atas ketiga
Pembahasan
Perbandingan nada-nada pada pipa organa terbuka (POB) memenuhi:

f_o : f₁ : f₂ : f₃ : ..... = 1 : 2 : 3 : 4 : .....

dengan:
f_o adalah frekuensi nada dasar
f₁ adalah frekuensi nada atas pertama
f₂ adalah frtekuensi nada atas kedua
dan seterusnya.

Perhatian !
(Sesuaikan lambang-lambang jika terdapat perbedaan, sebagian literature melambangkan nada dasar sebagai f₁)

a) Nada atas pertama (f₁)
f₁ / f_o = 2/1
f₁ = 2 × f_o = 2× 300 Hz = 600 Hz

b) Nada atas kedua ( f₂)
f₂/ f_o = 3 / 1
f₂ = 3 × f_o = 3 × 300 = 900 Hz

c) Nada atas ketiga
f₃/ f_o = 4 / 1
f₃ = 4 × f_o = 4 × 300 = 1200 Hz

Soal No. 2
Sebuah pipa organa yang tertutup salah satu ujungnya memiliki nada dasar dengan frekuensi sebesar 300 Hz. Tentukan besar frekuensi dari :
a) Nada atas pertama
b) Nada atas kedua
c) Nada atas ketiga

Pembahasan
Perbandingan nada-nada pada pipa organa tertutup (POT) memenuhi:

f_o : f₁ : f₂ : f₃ : ..... = 1 : 3 : 5 : 7 : .....

dengan:
f_o adalah frekuensi nada dasar
f₁ adalah frekuensi nada atas pertama
f₂ adalah frtekuensi nada atas kedua

a) Nada atas pertama (f₁)
f₁ / f_o = 3/1
f₁ = 3 × f_o = 3 × 300 Hz = 900 Hz

b) Nada atas kedua ( f₂)
f₂/ f_o = 5 / 1
f₂ = 5 × f_o = 5 × 300 = 1500 Hz

c) Nada atas ketiga
f₃/ f_o = 7 / 1
f₃ = 7 × f_o = 7 × 300 = 2100 Hz

Soal No. 3
Seutas dawai memiliki nada atas ketiga dengan frekuensi sebesar 600 Hz. Tentukan :
a) frekuensi nada atas kedua dawai
b) frekuensi nada dasar dawai

Pembahasan
Perbandingan nada-nada pada dawai, sama dengan perbandingan nada-nada pada pipa organa terbuka yaitu memenuhi:

f_o : f₁ : f₂ : f₃ : ..... = 1 : 2 : 3 : 4 : .....

Sehingga:
a) frekuensi nada atas kedua dawai f₂
f₂ / f₃ = 3 / 4
f₂ = ( 3 / 4 )× f₃ = (3/4) x 600 = 450 Hz

b) frekuensi nada dasar dawai f_o
f_o / f₃ = 1 / 4
f_o = ( 1 / 4 ) × f₃ = (1/4) x 600 = 150 Hz

Soal No. 4
Sebuah pipa organa tertutup memiliki panjang 50 cm. Jika cepat rambat bunyi di udara adalah 340 m/s, tentukan frekuensi pipa organa saat:
a) terjadi nada dasar
b) terjadi nada atas kedua

Pembahasan
Data:
Pipa Organa Tertutup
L = 50 cm = 0,5 m
ν = 340 m/s
a) f_o = .....Hz
b) f₂ = .....Hz
Agar tidak terlalu banyak rumus yang harus dihafal, perhatikan ilustrasi berikut:

Keterangan gambar:
Diawali dari SEPEREMPAT λ kemudian naik setengah-setengah untuk seterusnya;
L = 1/4 λ → saat Nada Dasar
L = 3/4 λ → saat Nada Atas Pertama
L = 5/4 λ → saat Nada Atas Kedua
L = 7/4 λ → saat Nada Atas Ketiga
L = 9/4 λ → saat Nada Atas Keempat
dan terusannya.

Untuk selanjutnya rumus yang akan digunakan adalah rumus yang sudah kita kenal sebelumnya, yaitu:

f = ν / λ

a) Dari ilustrasi diatas terlihat, saat terjadi nada dasar, pada pipa sepanjang L terjadi 1/4 gelombang.
L = 1/4 λ atau λ = 4L = 4(0,5) = 2 m

Sehingga:
f = ν / λ = 340 / 2 = 170 Hz

Frekuensi yang kita temukan ini adalah frekuensi nada dasar atau f_o

a) Dari ilustrasi diatas terlihat, saat terjadi nada atas kedua, pada pipa sepanjang L terjadi 5/4 gelombang.
L = 5/4 λ atau λ = 4/5 L = 4/5 (0,5) = 0,4 m

Sehingga:
f = ν / λ = 340 / 0,4 = 850 Hz

Frekuensi yang kita temukan ini adalah frekuensi nada atas kedua atau f₂

Soal No. 5
Sebuah pipa organa terbuka memiliki panjang 60 cm. Jika cepat rambat bunyi di udara adalah 340 m/s, tentukan frekuensi pipa organa saat terjadi nada atas kedua

Pembahasan
Sketsa nada-nada pada pipa organa terbuka:

Keterangan gambar:
Diawali dari SETENGAH λ kemudian naik setengah-setengah untuk seterusnya.
L = 1/2 λ → saat Nada Dasar
L = 2/2 λ → saat Nada Atas Pertama
L = 3/2 λ → saat Nada Atas kedua
L = 4/2 λ → saat Nada Atas Ketiga
L = 5/2 λ → saat Nada Atas Keempat
L = 6/2 λ → saat Nada Atas Kelima
dan terusannya.

Saat terjadi nada atas kedua, terlihat pada pipa organa sepanjang L terbentuk satu setengah atau 3/2 gelombang,
L = 3/2 λ atau λ = 2/3 L = 2/3 × 0,6 = 0,4 m

Sehingga:
f = ν / λ = 340 / 0,4 = 850 Hz

Frekuensi yang kita temukan ini adalah frekuensi nada atas kedua atau f2

Soal No. 6
Diberikan dua buah pipa organa yang pertama tertutup salah satu ujungnya, satu lagi terbuka kedua ujung dengan panjang 30 cm. Jika nada atas kedua pipa organa tertutup sama dengan nada atas ketiga pipa terbuka, tentukan panjang pipa organa yang tertutup!

Pembahasan
Pipa organa tertutup:
Nada atas kedua → L = 5/4 λ → λ = 4/5 L

f = ν / λ
f = ν / (4/5 L)

Pipa organa terbuka:
Nada atas ketiga → L = 2 λ → λ = 1/2 L = 1/2 (30) = 15 cm

f = ν / λ
f = ν / 15

Frekuensi kedua pipa adalah sama, disamakan saja:

Soal No. 7
Pipa organa terbuka A dan pipa organa tertutup-sebelah B mempunyai panjang yang sama. Perbandingan frekuensi nada atas pertama antara pipa organa A dan pipa organa B adalah....
A. 1 : 1
B. 2 : 1
C. 2 : 3
D. 3 : 2
E. 4 : 3
(UMPTN 1995)

Pembahasan
Pipa organa A terbuka:
Nada atas 1 → L = λ → λ = L

f = ν / L

Pipa organa B tertutup:
Nada atas 1 → L = 3/4 λ → λ = 4/3 L

f = ν / (4/3 L)

maka