Optimal Sound Matching Solutionthrough Helmholtz resonator theory 1. Basic theoryHelmholtz Resonator was invented for sound analysis by H. VON Helmholtz(18211894) Its applications are various from bell, violin, guitar and bass speaker cabinet. It features shorter neck and volume bottle than wave as shown below. Specific frequency depends on air volume in neck(weight) and volume in the bottle(spring) So specific frequency is calculated as below.a : Necks area ()V : Resonator volume ()L : Necks length (m)C : Sound velocity (344m/s)Therefore any shapes of resonator is not affecting Resonant Frequency. If the volume & necks length is same, the resonator has same resonant frequency even in different shape.Basic principleOptimal Sound Matching Solution through Helmholtz resonator theoryEx.1)Whats the resonant frequency in case of a bottle with outer dia. 9.8cm, neck length10cm, neck outer dia. 3cm? ExampleOptimal Sound Matching Solution through Helmholtz resonator theory2. Application(1) Inside structure of handseta : Hole total area (m2)SpeakerLCASEV:Front Volumea : Air HoleBack VolumeL : Case thickness (m)V : Front volume (m3)C : 344 m/s (RT 20)ApplicationOptimal Sound Matching Solution through Helmholtz resonator theory(2) Example model: SS1534P-008- SIZE : 15mm X 3.4 H- Fo : 850 Hz- Ze : 8 ohm(3) Test conditions* Input power :0.1W at 5cmBasic principleOptimal Sound Matching Solution through Helmholtz resonator theoryBKMode: TSRA: Frequency Response, Magn dB re 20.00Pa/V1002005001k2k5k10kHz60708090100110dBX:900.00Hz Y:98.92dB ZA:Live Curve TSR fund.SS1534P-008 GRAPH in BAFFLEOriginal test resultOptimal Sound Matching Solution through Helmholtz resonator theory(4) TEST according to some variations Basic Structure Air Hole quantity variation Case thickness variation Front Volume variation Back Volume variationTest conditionOptimal Sound Matching Solution through Helmholtz resonator theory Basic structurea : 1.55mm X 4 eaL : 1.55mmV : 1.2ccC : 344 m/s (RT 20)Back volume : 2.42cc=3,486HzBasic structureHand Set Matching Solution with Helmholtz resonatorSpeakerLCASEV:Front Volumea : Air HoleBack VolumeX:3.0000kHz Y:104.23dB ZA:Live Curve TSR fund.BKMode: TSRA: Frequency Response, Magn dB re 20.00Pa/V1002005001k2k5k10kHz60708090100110dB3,486Hz 3,000HzTest resultOptimal Sound Matching Solution through Helmholtz resonator theory Air Hole quantity variationa : 1.55mm X 4 ea 1.55mm X 2 eaL : 1.55mmV : 1.2ccC : 344 m/s (RT 20)Back volume: 2.42cc=2,465HzAir hole variationOptimal Sound Matching Solution through Helmholtz resonator theorySpeakerLCASEV:Front Volumea : Air HoleBack VolumeBKMode: TSRA: Frequency Response, Magn dB re 20.00Pa/V1002005001k2k5k10kHz60708090100110dBX:2.4000kHz Y:101.47dB ZA:Live Curve TSR fund.2,465Hz 2,400HzTest result of air hole changedHand Set Matching Solution with Helmholtz resonator Case thickness variationa : 1.55mm X 4 eaL : 1.55mm 2.5mmV : 1.2ccC : 344 m/s (RT 20)Back volume : 2.42cc=2,745HzCase thickness changedOptimal Sound Matching Solution through Helmholtz resonator theorySpeakerLCASEV:Front Volumea : Air HoleBack VolumeBKMode: TSRA: Frequency Response, Magn dB re 20.00Pa/V1002005001k2k5k10kHz60708090100110dBX:2.6000kHz Y:102.29dB ZA:Live Curve TSR fund.2,745Hz 2,600HzTest result by case thickness variationOptimal Sound Matching Solution through Helmholtz resonator theory Front Volume variationa : 1.55mm X 4 eaL : 1.55mmV : 1.2cc 0.8ccC : 344 m/s (RT 20)Back volume: 2.42cc=4,269HzFront volume variationOptimal Sound Matching Solution through Helmholtz resonator theorySpeakerLCASEV:Front Volumea : Air HoleBack VolumeBKMode: TSRA: Frequency Response, Magn dB re 20.00Pa/V1002005001k2k5k10kHz60708090100110dBX:3.9000kHz Y:105.25dB ZA:Live Curve TSR fund.4,269Hz 3,900HzTest result by front volume variationOptimal Sound Matching Solution through Helmholtz resonator theory Back Volume variationa : 1.55mm X 4 eaL : 1.55mmV : 1.2ccC : 344 m/s (RT 20) Back volume: 2.42cc 1.5cc Back volume variationOptimal Sound Matching Solution through Helmholtz resonator theorySpeakerLCASEV:Front Volumea : Air HoleBack VolumeBKMode: TSRA: Frequency Response, Magn dB re 20.00Pa/V1002005001k2k5k10kHz60708090100110dBX:1.3000kHz Y:96.65dB ZA:Live Curve TSR fund.Loss of low soundTest result by back volume changedOptimal Sound Matching Solution through Helmholtz resonator theory3. ConclusionWe come to conclusion through proved theory as follows:1) The quantity of front air hole , Resonant Frequency 2) Front case thickness , Resonant Frequency 3) Front volume , Resonant Frequency 4) Back volume , Low sound Optimal acoustic solution in handset design can be coming from Helmholtz resonator theory.q In case that speaker itself has flat frequency response, specific resonant frequency is generating when being mounted in the handset. Then SPL and sou