Answer:
4/10 of L.
Explanation:
A stopped pipe is a pipe with one closed end and one opened end. it is also called a closed pipe.
The fundamental mode of a stopped pipe is also called its fundamental frequency, and is f₁=v/4L.
Where f₁=fundamental frequency, v= velocity of sound, L= Length of pipe.
The fifth harmonic of the stopped pipe f₅ =5v/4L .................(1)
For an open pipe,
Fundamental mode is also called fundamental frequency f₁₀=v/2l₀ .......... (2)
Where f₁₀ = fundamental frequency of a closed pipe, v= velocity of sound and l₀=length of the resulting open pipe.
from the question, the fundamental mode of the resulting open pipe = The fifth harmonic of the original stopped pipe.
∴ f₅=f₁₀
⇒5v/4L = v/2l₀
Equating v from both side of the equation,
⇒ 5/4L = 1/2l₀
Cross multiplying the equation,
5×2l₀ = 4L× 1
10l₀ = 4L
Dividing both side of the equation by the coefficient of l₀ i.e 10
10l₀/10 = 4L/10
∴ l₀ = 4/10(L)
∴ 4/10 of L must be cut off
