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Martin King Mathcad Worksheet

Martin King Mathcad Worksheet: A Powerful Tool for Loudspeaker Design

If you are interested in designing and building your own loudspeakers, you may have heard of Martin King, a renowned expert in the field of quarter wavelength loudspeaker design. Martin King has developed a series of Mathcad worksheets that can simulate various types of quarter wavelength enclosures, such as transmission lines, tapered quarter wave tubes, and horn loaded designs. These worksheets are based on a calculation algorithm that is extremely flexible and accurate, allowing you to optimize your enclosure design for your chosen driver and your personal preferences.

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What is a Quarter Wavelength Loudspeaker?

A quarter wavelength loudspeaker is a type of loudspeaker that relies on a quarter wavelength acoustic standing wave inside the enclosure to produce the bass response. The most common example of this type of loudspeaker is a transmission line, which is a long and narrow tube filled with damping material and terminated with an open end or a port. The driver is mounted near one end of the tube, and the sound waves generated by the driver propagate along the tube until they reach the other end, where they are either radiated out or reflected back. The length of the tube determines the lowest frequency that can be reproduced by the enclosure, which is equal to one quarter of the wavelength of that frequency. For example, if the tube is 2.5 meters long, the lowest frequency that can be reproduced is about 34 Hz (assuming the speed of sound is 340 m/s).

Other types of quarter wavelength loudspeakers include tapered quarter wave tubes (TQWT), which are tubes that gradually decrease in cross-sectional area from the driver to the open end, and horn loaded designs, which are tubes that gradually increase in cross-sectional area from the driver to the open end. These variations affect the impedance and frequency response of the enclosure, as well as the efficiency and directivity of the sound radiation.

What are the Benefits of Quarter Wavelength Loudspeakers?

Quarter wavelength loudspeakers have several advantages over conventional closed or ported box designs. Some of these advantages are:

  • They can produce deep and natural bass with low distortion and minimal group delay.

  • They can reduce or eliminate unwanted resonances and standing waves inside the enclosure.

  • They can provide a smooth transition from the driver to the room acoustics.

  • They can offer a high degree of design flexibility and customization.

What are the Challenges of Quarter Wavelength Loudspeakers?

Despite their benefits, quarter wavelength loudspeakers also have some challenges that need to be addressed by careful design and construction. Some of these challenges are:

  • They require a lot of space and materials, as they tend to be large and heavy.

  • They are sensitive to driver parameters and placement, as well as damping material type and amount.

  • They are difficult to model mathematically, as they involve complex acoustic phenomena and interactions.

  • They may have limited bandwidth and efficiency, depending on the type and size of the enclosure.

How can Martin King Mathcad Worksheet Help?

Martin King Mathcad Worksheet is a powerful tool that can help you overcome these challenges and design your own quarter wavelength loudspeakers with confidence and ease. Using this tool, you can:

  • Select from various types of quarter wavelength enclosures, such as transmission lines, TQWTs, horn loaded designs, and more.

  • Enter your driver parameters and preferences, such as sensitivity, impedance, Qts, Vas, Fs, etc.

  • Optimize your enclosure dimensions and shape for your desired frequency response and impedance curve.

  • Visualize your enclosure performance using graphs and charts that show SPL, phase angle, group delay, impedance magnitude and phase, etc.

  • Compare different enclosure designs and drivers using side-by-side plots.

  • Export your enclosure data to other software tools or formats for further analysis or fabrication.

Where can I Get Martin King Mathcad Worksheet?

Martin King Mathcad Worksheet is available for purchase from Martin King's website [Quarter Wavelength Loudspeaker Design]. You will need to have Mathcad installed on your computer to use this tool. Mathcad is a software program that allows you to perform calculations, manipulate data, create graphs, and document your work in an easy-to-use interface. You can download a free trial version of Mathcad from [MathWorks](


Martin King Mathcad Worksheet is a valuable tool for anyone who wants to design and build their own quarter wavelength loudspeakers. It can help you simulate various types of enclosures, optimize your design parameters, and visualize your results. Whether you are a beginner or an expert, you can benefit from this tool and create your own high-quality loudspeakers that will satisfy your ears and impress your friends.


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