Modelling the sound of a drum head.

In summary: Your Name]In summary, Arthur is seeking help with creating a numerical model to synthesize the sound of a struck drum head using Mathematica. He has solved the wave equation for a circular membrane and obtained an amplitude function, but he is unsure how to convert this into a 1-dimensional time series for listening with speakers. He is also concerned about the accuracy of choosing an arbitrary point on the membrane for the amplitude function. You suggest using the amplitude function to modulate an audio signal generator and taking into account other factors such as material, tension, and size of the drum to fine-tune the sound.
  • #1
arth_e
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Please excuse me if this is not the most appropriate subforum for this question and please move it if necessary.

I am trying to make a numerical model with Mathematica to synthesize the sound of a struck drum head (circular membrane).

I solve the wave equation for a circular membrane to get a numerical function for amplitude u(time,position) which depends on some striking function f. But now I don't know how to convert the information to obtain a 1-dimensional time series that can be listened to with the speakers. I feel I am missing something fundamental here.

In the case of a string, one can pick any point on it x0 , and then the function u(t,x0) can be sent straight to the speakers provided x0 is not on a node of the string. I am guessing this is kind of the same way a guitar pick up works (?) . However in the case I of the drum, isolating an arbitrary point on the surface does not feel it should be physically accurate representation of the sound.

Looking forward to hear your opinion,

Arthur

edit: here is a java application that can produce a drum head sound http://www.falstad.com/circosc/
 
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  • #2


Hello Arthur,

Thank you for your question. It is great that you are using Mathematica to create a numerical model for the sound of a struck drum head. This is a complex problem, but I will try to provide some guidance on how to convert the numerical information into a 1-dimensional time series that can be listened to with speakers.

Firstly, it is important to note that the sound of a struck drum head is a result of a combination of different physical phenomena, such as the vibration of the membrane, the resonance of the drum body, and the air pressure changes inside the drum. Your numerical model should take all of these factors into account to accurately simulate the sound.

To convert the numerical information into a 1-dimensional time series, you will need to use the amplitude function u(time,position) that you have obtained from solving the wave equation for a circular membrane. This function represents the displacement of the membrane at a given time and position. To convert this into a sound signal, you can use the amplitude values to modulate an audio signal generator, such as a sine wave or white noise, to produce the sound of the drum.

The choice of the position on the membrane to use for the amplitude function will depend on the specific characteristics of the drum head you are trying to simulate. In the case of a guitar, the string is a one-dimensional object, so choosing any point on it will result in the same sound. However, for a drum head, the membrane is a two-dimensional object, so the position you choose will affect the sound produced. You can try different positions and see which one gives the most accurate representation of the sound.

In addition to the amplitude function, you will also need to consider other factors such as the material and thickness of the membrane, the tension of the drum head, and the size and shape of the drum body. These parameters will affect the frequency and amplitude of the sound produced. You can use these parameters in your numerical model to fine-tune the sound and make it more realistic.

I hope this helps you in your modeling process. Please let me know if you have any further questions or need more clarification. Best of luck with your project!
 

1. How does a drum head produce sound?

A drum head produces sound when it is struck by a drum stick or mallet. The force of the impact causes the drum head to vibrate, which creates sound waves that travel through the air and into our ears.

2. What factors affect the sound of a drum head?

The tension of the drum head, the material it is made of, and the shape and size of the drum all affect the sound of a drum head. The type of drum stick or mallet used can also impact the sound.

3. How can you model the sound of a drum head?

To model the sound of a drum head, you can use mathematical equations and computer simulations. These models take into account the physical properties of the drum head and the impact of the drum stick or mallet to predict the resulting sound wave.

4. What is the importance of modelling the sound of a drum head?

Modelling the sound of a drum head allows us to better understand the physics behind drumming and how different factors affect the sound produced. This knowledge can be used to improve the design and construction of drums and drum heads, as well as to enhance the playing experience for musicians.

5. Can modelling the sound of a drum head be used for other instruments?

Yes, the same principles and techniques used to model the sound of a drum head can be applied to other instruments, such as cymbals, bells, and even string instruments. This allows for a better understanding of how different musical instruments produce sound and can lead to improvements in their design and construction.

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