Find Length of Closed Pipe for Equal Frequency

[diracdelta]

Homework Statement

Open and closed pipe, give 5 beats per second.
Open pipe is 30 cm long and gives a tone of frequency f₀.
Speed of sound is 330 m/s.
How long do we need to extend closed pipe so both pipes give equal frequencies?

Homework Equations

Open pipe, f_n=n*f₁, f₁=v/(2L)
Closed pipe; f_n= f*f₁, f₁ = v/(4L)
f_beat = f₂ - f₁

The Attempt at a Solution

For open pipe, I assume that f₀ is f₁, or basic frequency.
f=v/2L=330 ms^-1 / 0,6 m = 550 Hz

f_beat = f₂ - f₁
5 = f₂ - 550 Hz
f₂ = 555 Hz.

Now we need to find the length of open pipe.
4L = v/f₂
l= v/4f₂= 0,15 m

Since i have the length of closed pipe, motive is to adjust it so we have frequency of 550 Hz.
4L = v/f₂,
4*L = 330 ms^-1/ 550 Hz
4*L = 0,6 m
L = 0,15

What did I do wrong?

 

[NascentOxygen]

Now we need to find the length of open pipe.

I think you mean closed pipe? Better check that calculation, too, using 555Hz. ☹

 

[ehild]

The Attempt at a Solution

For open pipe, I assume that f₀ is f₁, or basic frequency.
f=v/2L=330 ms^-1 / 0,6 m = 550 Hz

f_beat = f₂ - f₁
5 = f₂ - 550 Hz
f₂ = 555 Hz.

Now we need to find the length of open pipe.

You ment closed pipe, didn't you?

4L = v/f₂
l= v/4f₂=0,15 m

l= v/(4f₂)=330/(4*555)=0.1486 m
You rounded off too early, too much.

Since i have the length of closed pipe, motive is to adjust it so we have frequency of 550 Hz.
4L = v/f₂,
4*L = 330 ms^-1/ 550 Hz
4*L = 0,6 m
L = 0,15

What did I do wrong?

You rounded off too much.

 

[diracdelta]

I think you mean closed pipe? Better check that calculation, too, using 555Hz. ☹

Yes. lapsus linguae :D

You ment closed pipe, didn't you?l= v/(4f₂)=330/(4*555)=0.1486 m
You rounded off too early, too much.

You rounded off too much.

:(
I did it again, i got same result like yours.

Thanks for help guys.
You are the best :)

 

[HalfLostAndSearching]

Your calculations are correct, but the length of the closed pipe should be 0.3 m, not 0.15 m. This is because the length of the open pipe is 0.3 m, so the total length of the two pipes should be 0.3 m + 0.3 m = 0.6 m. Therefore, the length of the closed pipe should be 0.6 m - 0.3 m = 0.3 m.