Question

Two organ pipes are emitting their fundamental notes, when each closed at end, give 5 beats per sec. If their fundamental frequencies are 250 Hz and 255 Hz, then find the ratio of their lengths.

Options

• `49/50`

• `49/51`

• `50/51`

• `51/50`

Answer 1

`bb(51/50)`

Explanation:

Fundamental frequency of closed pipe = `"V"/(4"L")`

where V = velocity of sound/wave

L = Length of pipe

Let for first pipe length = L₁

frequency = f₁ = 250 H₂

For 2nd pipe = length = L₂

frequency = f₂ = 255 H₂

`"f"_1/"f"_2=("V"/(4"L"_1))/("V"/(4"L"_2))` 

⇒ `250/255="L"_2/"L"_1`

⇒ `50/51="L"_2/"L"_1`

⇒ `"L"_1/"L"_2=51/50`