Index VinylArm & Cartridge Resonance

Arm & Cartridge Resonance

Check that tonearm mass and cartridge compliance resonate in the safe window.

Resonant frequency8.7Hz

VerdictIdeal

Total moving mass18.5g

Arm mass for 8 to 12 Hz2 to 14g

Where the resonance falls

Green marks the 8 to 12 Hz target. The peak height is drawn for a typical lightly damped arm. Real peaks range from about 6 to 15 dB.

Input

Tonearm effective massg

From the arm's data sheet. Under 10 g is light, over 20 g is heavy.

Cartridge massg

Screws and headshell extrasg

Cartridge complianceµm/mN

Also written as ×10⁻⁶ cm/dyne. The number is the same.

Compliance was measured at 100 Hz

Common for Japanese cartridges. The value is multiplied by 1.75 to estimate the 10 Hz figure; this is an approximation.

How it works

A mass on a spring

The stylus cantilever is held by a rubber suspension, which is a spring. The cartridge body and the tonearm hang on that spring as a mass. Like any mass on a spring, they resonate:

f_0 = \frac{1}{2\pi\sqrt{M\,C}}

With mass $M$ in grams and compliance $C$ in µm/mN (the same number as compliance units of 10⁻⁶ cm/dyne), this becomes the working formula

f_0 = \frac{1000}{2\pi\sqrt{(m_{arm} + m_{cart} + m_{hw})\,C}} \approx \frac{159}{\sqrt{M\,C}}\ \mathrm{Hz}

The safe window

At resonance the arm and stylus move against each other with several times the normal amplitude. Two things must be avoided:

Below about 7 Hz lie record warps and footfall. A resonance here makes the woofers pump and can throw the stylus out of the groove.
Above about 14 Hz the resonance begins to boost the lowest recorded bass and colours the sound.

The accepted target is 8 to 12 Hz, with 10 Hz as the centre.

Matching rules

High-compliance cartridges (soft suspension, 20 and above) suit light arms. Low-compliance moving coils (10 or less) need heavy arms. If the result is too high, add mass at the headshell; if too low, the only real cure is a lighter arm or a stiffer cartridge.

Check which frequency the maker used. Static or 10 Hz compliance is what the formula needs. Figures given at 100 Hz are lower, typically by a factor of 1.5 to 2.