Help with standing waves question

In summary, the conversation discusses the formation of a standing wave in a glass tube filled with water when a small loudspeaker emits a sound of frequency 425 Hz. The question raised is how to determine the wavelength of the sound, which is calculated using the formula v = fλ. The book's worked example shows that at a water level of 20cm, the wavelength must be 80cm. The question is then raised about whether this is always the fundamental frequency or if it is dependent on the length of the closed tube. The conclusion is that the first input of sound will always be the fundamental frequency, as shown by the fact that the tube only resonated at a length of 20cm.
  • #1
Vandalus
7
0
A small loudspeaker connected to a signal generator emits a sound of frequency 425 Hz. It is fixed above a long glass tube that is filled with water and has a drain at the bottom so that the water can be slowly released from it. When the level has fallen 20cm from the top of the tube, a standing wave is formed and the air column resonates.

Calculate the wavelength of the sound.

v = fλ

In my book's worked example it says that:

λ/4 = 20cm therefore the λ must be 80cm.

What I don't understand is this:

How do you know that at 20 cm, the standing wave generated will definitely be the first harmonic/fundamental frequency since λ/4 only applies if the standing wave generated is the fundamental frequency?

Isn't 20cm just an arbitrary number?

Or is it that no matter how much the water level falls (no matter the length of the closed tube) the first input of sound will definitely be the fundamental frequency?

Any help is greatly appreciated :D
 
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  • #2
Vandalus said:
Or is it that no matter how much the water level falls (no matter the length of the closed tube) the first input of sound will definitely be the fundamental frequency?

Yes. It's the (implied) fact that it did not resonate at any shorter length. Had 20cm been, say, the third harmonic, it would have resonated at 4cm.
 
  • #3
Ah ok. Looks like I should learn to read questions more thoroughly aha.

Thanks :D
 

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. This results in a pattern of nodes and antinodes where the amplitude of the wave remains constant in specific points.

2. How are standing waves formed?

Standing waves are formed when two waves with the same frequency and amplitude travel in opposite directions and intersect with each other. The points where the waves meet and interfere constructively create nodes, while the points where they interfere destructively create antinodes.

3. What factors affect the formation of standing waves?

The formation of standing waves is affected by the frequency and amplitude of the two waves, as well as the medium through which they are traveling. The length and tension of the medium also play a role in determining the specific pattern of nodes and antinodes that form.

4. What are some real-life examples of standing waves?

Standing waves can be observed in various situations, such as in musical instruments like guitars or string instruments, where the strings vibrate at specific frequencies and create nodes and antinodes. They can also be seen in microwave ovens, where the microwaves bounce back and forth between the walls of the oven, creating standing waves that cook the food evenly.

5. How are standing waves useful in scientific research?

Standing waves have many practical applications in scientific research. They are used in fields such as acoustics, optics, and quantum mechanics to study the properties of waves and their interactions. They are also useful in studying the behavior of materials and structures, as well as in medical imaging techniques like ultrasound.

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