Standing waves - True or false?

In summary, the frequencies of the third and fifth harmonics in a pipe open at both ends are not necessarily three and five times the fundamental frequency, respectively. It depends on the length of the pipe and the speed of sound. In a pipe open at one end and closed at the other, only the odd harmonics are excited.
  • #1
sonutulsiani
138
0

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?
 
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  • #2
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. :smile:)
 
  • #3
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.
 
  • #4
What equation do you have for getting frequencies or wavelengths in pipes with the ends both open or both closed?
 
  • #5
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
 
  • #6
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).
 
  • #7
I didn't understand what you just said. Please help me, I have to submit my homework today.
 
  • #8
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
 
Last edited by a moderator:
  • #9
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
 

Related to Standing waves - True or false?

1. What are standing waves?

Standing waves are a type of wave that occurs when two waves with the same frequency and amplitude travel in opposite directions and interfere with each other, resulting in a stationary wave pattern.

2. Are standing waves real or just a theoretical concept?

Standing waves are a real phenomenon that can be observed in many different systems, including musical instruments, electromagnetic fields, and water waves.

3. How do standing waves differ from other types of waves?

Unlike other waves, standing waves do not propagate through space. Instead, they oscillate in place, with certain points called "nodes" remaining stationary while other points called "anti-nodes" oscillate with maximum amplitude.

4. Can standing waves only occur in specific types of mediums?

Standing waves can occur in any medium that can support wave propagation, such as air, water, or solids. The conditions for standing waves to form may vary depending on the medium, but the underlying principle remains the same.

5. Are standing waves only formed by two waves traveling in opposite directions?

No, standing waves can also be formed by the interference of multiple waves with the same frequency and amplitude. In this case, the resulting standing wave will have multiple nodes and anti-nodes.

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