Standing waves - True or false?

[sonutulsiani]

Homework Statement

Consider standing waves in an organ pipe. True or false:

1. In a pipe open at both ends, the frequency of the third harmonic is three times that of the first harmonic.

2. In a pipe open at both ends, the frequency of the fifth harmonic is five times that of the fundamental.

3. In a pipe that is open at one end and stopped at the other, the even harmonics are not excited.

Homework Equations

The Attempt at a Solution

I got it as

1. False
2. False
3. True

Are they right?

 

[Redbelly98]

Can you show how you got those answers / why you think their true?

(Unfortunately, telling you if they are wrong or right is the same as giving you the correct answers. )

 

[sonutulsiani]

Well I actually guessed the 1st and 2nd. But in the 3rd when one end is open and other is closed only the odd harmonics are there. Hint me on 1st and 2nd.

 

[Redbelly98]

What equation do you have for getting frequencies or wavelengths in pipes with the ends both open or both closed?

 

[sonutulsiani]

I have no idea when they are both open, it's not there in my book. But for closed, f1 = V/2L,
f2=2V/2L, f3= 3V/2L

 

[Fightfish]

It's good to derive the relations yourself. This can be easily done through diagrams, and then applying the boundary conditions eg. for an open pipe, both ends of the pipe must correspond to the displacement antinodes (ignoring end corrections for now).

 

[sonutulsiani]

I didn't understand what you just said. Please help me, I have to submit my homework today.

 

[Fightfish]

Examples of some diagrams for both open and closed (at one end) pipes here:
http://www.eng.cam.ac.uk/DesignOffice/mdp/electric_web/AC/02375.png

 

[sonutulsiani]

According to this it should be false both of them right?
Because 3rd harmonic freq will be V/L and 5th harmonic freq will be 2 V/L