CN103813260B - A kind of long spacing reverberation time preparation method based on image source method - Google Patents

Abstract

Based on a long spacing reverberation time preparation method for image source method, relate to the preparation method of a kind of long spacing reverberation time.It obtains the large problem of the error of long spacing reverberation to solve existing method.It is by the long spacing with geometry reflecting boundary, layout points sound source (m, n) and the acceptance point apart from this mirror image sound source z position; Then calculate according to the Distance geometry acoustic energy of point sound source (m, n) to acceptance point, the final acquisition long spacing reverberation time.The present invention is applicable to obtain subway station, corridor isometric spatial-acoustic reverberation time.

Description

A kind of long spacing reverberation time preparation method based on image source method

Technical field

The present invention relates to a kind of long spacing reverberation time preparation method.

Background technology

At present, existing reverberation time preparation method adopts classical acoustic theoretical, it is applicable to the performing art space that cinema, arenas, auditorium etc. are taken as the leading factor with acoustic design, but and acquisition that the is inapplicable and reverberation time of the extensive long spacing existed in large public building.Should the method for classical acoustic theory, the error of its long spacing reverberation obtained is larger.

Summary of the invention

The present invention is the problem that the error in order to solve the reverberation of existing method acquisition long spacing is large, thus provides a kind of long spacing reverberation time preparation method based on image source method.

Based on a long spacing reverberation time preparation method for image source method, it comprises the following steps:

Step one, in the long spacing with geometry reflecting boundary, layout points sound source (m, n) and the acceptance point apart from this mirror image sound source z position; Described point sound source and acceptance point mirror image sound source each other;

Distance D between mirror image sound source (m, n) and acceptance point _{z, m, n}for:

$D_{z,m,n}=\sqrt{{\left[b\right|m-g\left(m\right)|+2L_b\frac{m}{\left|m\right|}g\left(m\right)]}^2+\left[a\right|n-g\left(n\right)|+2L_a\frac{n}{\left|n\right|}g{\left(n\right)]}^2+z^2}$

M and n is integer; And m and n is all not equal to 0;

When m is odd number, g (m)=1; When x is even number, g (m)=0;

When n is odd number, g (n)=1; When x is even number, g (n)=0;

A and b is height and the width in the long spacing cross section with geometry reflecting boundary;

L _ait is the distance of the ceiling of the long spacing of point sound source and geometry reflecting boundary;

L _bit is the distance of the side wall of the long spacing of point sound source and geometry reflecting boundary;

Step 2, timing definition direct sound wave being arrived acceptance point are t=0, then the reflected sound of point sound source (m, n) arrives the time t of acceptance point _{z, m, n}obtained by following formula:

$t_{z,m,n}=\frac{D_{z,m,n}}{c}-\frac{z}{c}$

In formula: c is the velocity of sound, 340m/s;

Then: between time t to t+ △ t, point sound source (m, n) to the acoustic energy of acceptance point is:

$E_{z,m,n}=\frac{K_W}{{D_{z,m,n}}^2}{(1-\mathrm{\α})}^{\left|m\right|+\left|n\right|}$

Wherein: t≤t _{z, m, n}<t+ △ t; K _wbe the constant relevant with the acoustical power of sound source, α is the acoustic absorptivity at interface; △ t is incremental time;

E in other situation _{z, m, n}be 0;

Step 3, between time t and t+ △ t, adopt formula:

${L\left(t\right)}_z=10\log \left[\underset{m=-\&infin;}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\underset{n=-\&infin;}{\overset{\&infin;}{\mathrm{\&Sigma;}}}{e}^{-{\mathrm{MD}}_{z,m,n}}{E}_{z,m,n}\right]$

Calculate the continuous sound pressure level L of equivalence at acceptance point place _eqreverberation time L (t) _z;

Step 4, the continuous sound pressure level L of equivalence at acceptance point place that step 3 is obtained _eqreverse integral is adopted to obtain the reverberation time L of steady-state sound pressure level _z,

$L_z=10\log \underset{\mathrm{\&Delta;t}}{\mathrm{\&Sigma;}}{10}^{{L\left(t\right)}_z/10}-L_{\mathrm{ref}}$

In formula: L _reffor reference sound intensity is arbitrarily downgraded;

Obtain the long spacing reverberation time based on image source method.

Point sound source is arranged in the center in the long spacing cross section with geometry reflecting boundary;

Average reflection distance D then between time t and t+ △ t ₀, the approximate number N of mirror image sound source and mirror image sound source average exponent number R obtains by following formula respectively:

$D_0=c(\frac{z}{c}+t+\frac{1}{2}\mathrm{\&Delta;t});$

The approximate number N of mirror image sound source is obtained by following formula:

$\begin{array}{c}N=\frac{1}{S}\left\{\mathrm{\&pi;}\right[c^2{(\frac{z}{c}+t+\mathrm{\&Delta;t})}^2-z^2]-\mathrm{\&pi;}[c^2{(\frac{z}{c}+t)}^2-z^2\left]\right\}\\ =\frac{\mathrm{\&pi;}{c}^2}{S}[2(\frac{z}{c}+t)+\mathrm{\&Delta;t}]\mathrm{\&Delta;t}\end{array};$

In formula: z/c is the time of advent of direct sound wave; S is cross sectional area;

Mirror image sound source average exponent number R is obtained by following formula:

$R=\frac{2\mathrm{\&Delta;\&theta;}}{\mathrm{\&pi;}}\underset{\mathrm{\&theta;}=0,\mathrm{step}:\mathrm{\&Delta;\&theta;}}{\overset{\frac{\mathrm{\&pi;}}{2}}{\mathrm{\&Sigma;}}}(\frac{D_p\sin \mathrm{\&theta;}}{a}+\frac{D_p\cos \mathrm{\&theta;}}{b});$

In formula: the angle determining mirror image sound source position, D _pd ₀to the projection of mirror image sound source plane; Step is step-length;

$D_p=\frac{1}{2}[\sqrt{c^2{(\frac{z}{c}+t+\mathrm{\&Delta;t})}^2-z^2}+\sqrt{c^2{(\frac{z}{c}+t)}^2-z^2}]$

Work as D _pwhen >>a, b, reverberation time L (t) _zpass through formula:

$L{\left(t\right)}_z=10\log \left[N\frac{K_W}{{D_0}^2}{(1-\mathrm{\&alpha;})}^R\right]-{\mathrm{MD}}_0$

Obtain.

The wall with the long spacing two ends of geometry reflecting boundary at point sound source place is reflection metope; Comprising (2G+1) individual mirror image sound source, G is integer; Form (2G+1) individual mirror image sound source plane, then reverberation time L (t) _zpass through formula:

${L\left(t\right)}_z=10\log \underset{q=-G}{\overset{G}{\mathrm{\&Sigma;}}}{(1-{\mathrm{\&alpha;}}_e)}^{\left|q\right|}{10}^{L{\left(t^{\&prime;}\right)}_{z_q}/10}$

Obtain;

In formula: q is mirror image sound source plane exponent number, α _ethe acoustic absorptivity of long spacing headwall, z _qit is the distance between q rank mirror image sound source and acceptance point;

Z _qvalue be:

$z_q=L|q-g\left(q\right)|+2d_s\frac{q}{\left|q\right|}g\left(q\right)$

In formula, d _sbe the distance of point sound source to long spacing headwall, L is long spacing length;

Q is integer, and q ≠ 0;

When q is odd number, g (q)=1; When q is even number, g (q)=0;

the sound pressure level that q rank mirror image sound source plane sends between time t and t+ △ t, wherein z=z _q, and

$t^{\&prime;}=t-\frac{z_q-z}{c}\&GreaterEqual;0.$

The present invention is based on mirror image sound source statistical method to obtain the long spacing reverberation time, resultant error is significantly improved relative to prior art, and with the results contrast of on-the-spot field survey, error amount is within 10%.

Accompanying drawing explanation

Fig. 1 is point sound source and the distribution schematic diagram of acceptance point in long spacing;

Fig. 2 is the distribution schematic diagram of mirror image sound source in long spacing;

Fig. 3 be in embodiment one when the center of point sound source in cross section, to the acquisition principle schematic of infinite spatial;

Fig. 4 be in embodiment one when the center of point sound source in cross section, in infinite spatial, average reflection distance D time between time t and t+ △ t ₀, calculate the approximate number N of mirror image sound source, the principle schematic of the average exponent number R of mirror image sound source.

Embodiment

Embodiment one, a kind of long spacing reverberation time preparation method based on image source method,

1, each mirror image sound source is considered

In the long spacing with geometry reflecting boundary, the distribution of mirror image sound source as shown in Figure 1.If point sound source is at distance ceiling L _a, distance side wall L _bposition on, acceptance point, on the position of distance sound source z, and is in the center in cross section.Distance D between mirror image sound source (m, n) and acceptance point _{z, m, n}for:

$D_{z,m,n}=\sqrt{{\left[b\right|m-g\left(m\right)|+2L_b\frac{m}{\left|m\right|}g\left(m\right)]}^2+\left[a\right|n-g\left(n\right)|+2L_a\frac{n}{\left|n\right|}g{\left(n\right)]}^2+z^2}$

(m,n＝-∞...∞) (1)

In formula: when x is odd number, g (x)=1; When x is even number, g (x)=0;

In formula: a and b is height in cross section and width.

If the arrival acceptance point timing definition of direct sound wave is t=0, so the reflected sound of mirror image sound source (m, n) arrives the time of acceptance point is t _{z, m, n}

$t_{z,m,n}=\frac{D_{z,m,n}}{c}-\frac{z}{c}---\left(2\right)$

Between time t to t+ △ t, mirror image sound source (m, n) to the acoustic energy of acceptance point is:

$E_{z,m,n}=\frac{K_W}{{D_{z,m,n}}^2}{(1-\mathrm{\&alpha;})}^{\left|m\right|+\left|n\right|}$ As t≤t _{d, m, n}<t+ △ t (3)

E in other situation _{z, m, n}be 0.(4)

In formula, K _wbe the constant relevant with the acoustical power of sound source, α is the acoustic absorptivity at interface, supposes that the acoustic absorptivity at all interfaces is identical, and has nothing to do with angle.

Between time t and t+ △ t, the L at the acceptance point place of short time _eq(equivalence is sound pressure level continuously) is calculated as:

${L\left(t\right)}_z=10\log \left[\underset{m=-\&infin;}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\underset{n=-\&infin;}{\overset{\&infin;}{\mathrm{\&Sigma;}}}{e}^{-{\mathrm{MD}}_{z,m,n}}{E}_{z,m,n}\right]--\left(5\right)$

In formula, M is the coefficient relevant with attenuation of air.Obtain the reverberation time by formula (5) available reverse integration, steady-state sound pressure level can be calculated as follows:

$L_z=10\log \underset{\mathrm{\&Delta;t}}{\mathrm{\&Sigma;}}{10}^{{L\left(t\right)}_z/10}-L_{\mathrm{ref}}---\left(6\right)$

L in formula _reffor reference sound intensity is arbitrarily downgraded.

2, mirror image sound source statistical method

Adopt statistical method can simplify above calculating.The basic thought of this method calculates the average reflection distance D between time t and t+ △ t ₀, calculate the approximate number N of mirror image sound source, the average exponent number R of mirror image sound source.

When the center of point sound source in cross section, to infinite spatial, as shown in Fig. 2 .5, D ₀, N and R can be calculated as follows:

$D_0=c(\frac{z}{c}+t+\frac{1}{2}\mathrm{\&Delta;t})---\left(7\right)$

$\begin{array}{c}N=\frac{1}{S}\left\{\mathrm{\&pi;}\right[c^2{(\frac{z}{c}+t+\mathrm{\&Delta;t})}^2-z^2]-\mathrm{\&pi;}[c^2{(\frac{z}{c}+t)}^2-z^2\left]\right\}\\ =\frac{\mathrm{\&pi;}{c}^2}{S}[2(\frac{z}{c}+t)+\mathrm{\&Delta;t}]\mathrm{\&Delta;t}\end{array}---\left(8\right)$

$R=\frac{2\mathrm{\&Delta;\&theta;}}{\mathrm{\&pi;}}\underset{\mathrm{\&theta;}=0,\mathrm{step}:\mathrm{\&Delta;\&theta;}}{\overset{\frac{\mathrm{\&pi;}}{2}}{\mathrm{\&Sigma;}}}(\frac{D_p\sin \mathrm{\&theta;}}{a}+\frac{D_p\cos \mathrm{\&theta;}}{b})---\left(9\right)$

In formula (7) and (8), z/c is the time of advent of direct sound wave.S is cross sectional area.In formula (9) the angle determining mirror image sound source position, D _pd ₀to the projection of mirror image sound source plane.

$D_p=\frac{1}{2}[\sqrt{c^2{(\frac{z}{c}+t+\mathrm{\&Delta;t})}^2-z^2}+\sqrt{c^2{(\frac{z}{c}+t)}^2-z^2}]---\left(10\right)$

D _pwhen >>a, b, L (t) _zcalculate by following formula:

$L{\left(t\right)}_z=10\log \left[N\frac{K_W}{{D_0}^2}{(1-\mathrm{\&alpha;})}^R\right]-{\mathrm{MD}}_0---\left(11\right)$

When the wall at long spacing two ends is for reflection metope, more mirror image sound source plane should be considered.If consider (2G+1) individual mirror image sound source plane, so formula (11) is then:

${L\left(t\right)}_z=10\log \underset{q=-G}{\overset{G}{\mathrm{\&Sigma;}}}{(1-{\mathrm{\&alpha;}}_e)}^{\left|q\right|}{10}^{L{\left(t^{\&prime;}\right)}_{z_q}/10}---\left(13\right)$

In formula, q is mirror image sound source plane exponent number, α _ethe acoustic absorptivity of long spacing headwall, z _qit is the distance between q rank mirror image sound source and acceptance point.Z _qcalculate with following formula:

$z_q=L|q-g\left(q\right)|+2d_s\frac{q}{\left|q\right|}g\left(q\right)---\left(14\right)$

In formula, d _sthe distance that sound source arrives long spacing headwall, the same formula of g (q) value (2).

In formula (13), be the sound pressure level that q rank mirror image sound source plane sends between time t and t+ △ t, available formula (11) calculates, wherein z=z _q, and:

$t^{\&prime;}=t-\frac{z_q-z}{c}\&GreaterEqual;0---\left(15\right)$

The present invention has carried out long spacing acoustics and has calculated and field survey in several subway station and corridor, and measurement result shows, the result of computational methods of the present invention and the error of actual measured value are within 10%.

Claims (3)

1., based on a long spacing reverberation time preparation method for image source method, it is characterized in that: it comprises the following steps:

Step one, in the long spacing with geometry reflecting boundary, layout points sound source (m, n) and the acceptance point apart from this point sound source z position; Described point sound source and acceptance point mirror image sound source each other;

Distance D between point sound source (m, n) and acceptance point _{z, m, n}for:

$D_{z,m,n}=\sqrt{{\left[b\right|m-g\left(m\right)|+2L_b\frac{m}{\left|m\right|}g\left(m\right)]}^2+{\left[a\right|n-g\left(n\right)|+2L_a\frac{n}{\left|n\right|}g\left(n\right)]}^2+z^2}$

M and n is integer; And m and n is all not equal to 0;

When m is odd number, g (m)=1; When m is even number, g (m)=0;

When n is odd number, g (n)=1; When n is even number, g (n)=0;

A and b is height and the width in the long spacing cross section with geometry reflecting boundary;

L _ait is the distance of the ceiling of the long spacing of point sound source and geometry reflecting boundary;

L _bit is the distance of the side wall of the long spacing of point sound source and geometry reflecting boundary;

Step 2, timing definition direct sound wave being arrived acceptance point are t=0, then the reflected sound of point sound source (m, n) arrives the time t of acceptance point _{z, m, n}obtained by following formula:

$t_{z,m,n}=\frac{D_{z,m,n}}{c}-\frac{z}{c}$

In formula: c is the velocity of sound, 340m/s;

Then: at t≤t _{z, m, n}during <t+ △ t, point sound source (m, n) to the acoustic energy of acceptance point is:

$E_{z,m,n}=\frac{K_W}{{D_{z,m,n}}^2}{(1-\mathrm{\&alpha;})}^{\left|m\right|+\left|n\right|}$

Wherein: K _wbe the constant relevant with the acoustical power of sound source, α is the acoustic absorptivity at interface; △ t is incremental time;

E in other situation _{z, m, n}be 0;

Step 3, between time t and t+ △ t, adopt formula:

$L{\left(t\right)}_z=10\log \left[\underset{m=-\&infin;}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\underset{n=-\&infin;}{\overset{\&infin;}{\mathrm{\&Sigma;}}}{e}^{{-\mathrm{MD}}_{z,m,n}}{E}_{z,m,n}\right]$

Calculate the continuous sound pressure level L of equivalence at acceptance point place _eqreverberation time L (t) _z; In formula, M is the coefficient relevant with attenuation of air;

Step 4, the continuous sound pressure level L of equivalence at acceptance point place that step 3 is obtained _eqreverse integral is adopted to obtain the reverberation time L of steady-state sound pressure level _z,

$L_z=10\log \underset{\mathrm{\&Delta;t}}{\mathrm{\&Sigma;}}{10}^{L{\left(t\right)}_z/10}-L_{\mathrm{ref}}$

In formula: L _reffor reference sound intensity is arbitrarily downgraded;

Obtain the long spacing reverberation time based on image source method.

2. a kind of long spacing reverberation time preparation method based on image source method according to claim 1, is characterized in that point sound source is arranged in the center in the long spacing cross section with geometry reflecting boundary;

Average reflection distance D then between time t and t+ △ t ₀obtained by following formula:

$D_0=c(\frac{z}{c}+t+\frac{1}{2}\mathrm{\&Delta;t});$

The approximate number N of mirror image sound source is obtained by following formula:

$\begin{array}{c}N=\frac{1}{S}\left\{\mathrm{\&pi;}\right[c^2{(\frac{z}{c}+t+\mathrm{\&Delta;t})}^2-z^2]-\mathrm{\&pi;}[c^2{(\frac{z}{c}+t)}^2-z^2\left]\right\}\\ =\frac{\mathrm{\&pi;}{c}^2}{S}[2(\frac{z}{c}+t)+\mathrm{\&Delta;t}]\mathrm{\&Delta;t}\end{array};$

In formula: z/c is the time of advent of direct sound wave; S is cross sectional area;

Mirror image sound source average exponent number R is obtained by following formula:

$R=\frac{2\mathrm{\&Delta;\&theta;}}{\mathrm{\&pi;}}\underset{\mathrm{\&theta;}=0,\mathrm{step}:\mathrm{\&Delta;\&theta;}}{\overset{\frac{\mathrm{\&pi;}}{2}}{\mathrm{\&Sigma;}}}(\frac{D_p\sin \mathrm{\&theta;}}{a}+\frac{D_p\cos \mathrm{\&theta;}}{b});$

In formula: θ is the angle determining mirror image sound source position, D _pd ₀to the projection of mirror image sound source plane; Step is step-length;

$D_p=\frac{1}{2}[\sqrt{c^2{(\frac{z}{c}+t+\mathrm{\&Delta;t})}^2-z^2}+\sqrt{c^2{(\frac{z}{c}+t)}^2-z^2}]$

Work as D _pwhen >>a, b, reverberation time L (t) _zpass through formula:

$L{\left(t\right)}_z=10\log \left[N\frac{K_W}{{D_0}^2}{(1-\mathrm{\&alpha;})}^R\right]-{\mathrm{MD}}_0$

Obtain.

3. a kind of long spacing reverberation time preparation method based on image source method according to claim 1, is characterized in that the wall with the long spacing two ends of geometry reflecting boundary at point sound source place is for reflection metope; Comprising (2G+1) individual mirror image sound source, G is integer; Form (2G+1) individual mirror image sound source plane, then reverberation time L (t) _zpass through formula:

$L{\left(t\right)}_z=10\log \underset{q=-G}{\overset{G}{\mathrm{\&Sigma;}}}{(1-{\mathrm{\&alpha;}}_e)}^{\left|q\right|}{10}^{L{\left(t^{\&prime;}\right)}_{z_q}/10}$

Obtain;

In formula: q is mirror image sound source plane exponent number, α _ethe acoustic absorptivity of long spacing headwall, z _qit is the distance between q rank mirror image sound source and acceptance point;

Z _qvalue be:

$z_q=L|q-g\left(q\right)|+2d_s\frac{q}{\left|q\right|}g\left(q\right)$

In formula, d _sbe the distance of point sound source to long spacing headwall, L is long spacing length;

Q is integer, and q ≠ 0;

When q is odd number, g (q)=1; When q is even number, g (q)=0;

the sound pressure level that q rank mirror image sound source plane sends between time t and t+ △ t, wherein z=z _q, and

$t^{\&prime;}=t-\frac{z_q-z}{c}\&GreaterEqual;0.$