The specific response of a dynamic receiver at low frequencies(within the range of stiffness control) when it is used as a telephone receiver has been studied by calculation. First, it is shown that the motional impedance of a telephone receiver is negligibly small as compared with the resistance of a moving coil. An expression of the specific response q_0 of the dynamic receiver with a vibrating system of three degrees of freedom has been worked out as a function of various constants of vibrating and driving systems on the supposition that the motional impedance and reactance of the receiver are negligibly small as compared with the resistance of a moving coil(namely, zero frequency). Then, some numerical example of the specific response q_0 are shown graphically as a function of the thickness h of a diaphragm with the mass ratio α of coil to diaphragm and the ratio of inner radius to outer radius of the diaphragm used as parameters. Further, using the expression of the response, maximum conditions of the response for the radius a of a diaphragm and the mass m_c of a moving coil have been worked out by calculating δ(q_0)/δa and δ(q_0)/δ(m_c), and numerical examples of the potimum condetion and the threshold value of response which are useful for design work are shown graphically as a function of the thickness of the deaphragm. The results are as follow;(1)If the mass of coil is held constant, a moving coil made of aluminium provides about 3 dB higher response than a moving coil made of copper. (2)The specific response can be increased by reducing the thickness of a diaphragm. (3)Both a_m and α_m are increased by reducing the thickness of a diaphragm, where the suffix m shows the maximum condition of each quantity. (4)When h&lt0. 09 mm and m_c&gt0. 4g, a_m is larger than 2. 5cm. On the basis of these results, the process of designing a dynamic receiver for telephone set is described. An experimental value of the specific response of a prototype receiver was compared with the value calculated from the above expression, resulting in good coincidence with each other.

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I)Introduction Reproduction of recorded sound on disk records causes tracing distortion. Recently some record makers have published their recording techniques to reduce tracing distortion by means of corrected recording signals. Different methods for obtaining the corrected signals have been proposed by RCA Laboratory and Telefunken Laboratory. A new recording technique was devised by Toshiba Central Research Lab. Several methods have been thought out to obtain the corrected recording signals, for example 1) phase modulation 2) correction terms obtained by Fourier expansion are added to the original recording signals. 3) correction terms are obtained by Taylor expansion of recording signals at the point where a modulated groove wall comes into contact with a reproducing spherical stylus. Method 3) was realized with comparatively simple electronic circuits, which can erovide corrected signals even when other causes of distortion have to be taken into account. II)Method to calculate corrected signals Assume that a spherical repoducing stylus S with a redius of r contacts with a modulated groove wall W(x) rigidly. (Fig. 1)The reproduced signal P(x) can be expressed in the form P(x-Δx)=W(x)-r1-cosθ) (1) In order that P(x-Δx) agrees well with R(x-Δx), W(x) must be in the following relation. W(x)=R(x-Δx)+r1-cosθ) (2) When both x and θ are small, corrected signals which are the sum of the original recording signals and correction terms, can be obtained approximately by Taylor expansion. W(x)=R(x)-rホsec{dR(x)/dx}-1]+(1/2)r^2sin^2{dR(x)/dx}ヤ^2R(x)/dx^2 (8) III)Calculation of harmonic distortion of a sinusoidal wave Let an input signal be denoted by R(x)=Aンin(γx), then corrected recording signals are given in the form W(x)=Aンin(γx)-rホsec{Aγャos(γx)}-1]-(1/2)r^2A^3γ^4cos^2(γx)ンin(γx) (10) Hence, reproduced signals are, P(x-Δx)=Aンin(γx)-rホsec{Aγャos(γx)}-1]-(1/2)r^2A^3γcos^2(γx)ラn(γx)+r/√&lt1+E^2&gt where, E=dW(x)/dx, and Δx=γE/√&lt1+E^2&gt. Percent harmonic distortion can be obtained by Fourier expansion of these signals. Denoting γA by Θ, and rγ^2A by η, Fig. 3(a)-(f) show the 2nd and 3rd harmonics in Θ-η coordinates. These graphs show a remarkable decrease in harmonics, especially in the 2nd harmonics, compered with signals to which no correction term is applied. In order to express corrected signals by Eq. (8), the following limitations are required; Θ≦1/2, η≦1 and A≦50, where η is the ratio of the radius of a spherical stylus to the minimum radius of curvature of a modulated groove wall. Even harmonics (2nd and 4th) and odd harmonics (3rd and 5th) are given in A-γ coordinates under the new limitations as shown in Fig. 4. Higher frequency or larger amplitude is available than in an uncorrected groove under the same distortion factor. γ is a function of signal frequency f, the radius of a groove R and the number of revolutions of a disk N. Fig. 5 shows the relation between γ, f and R, when N=33/3 rpm. IV)IM distortion Fig. 6 shows the calculated value of intermodulation distortion for harmonic signals of 400 and 4000 cps at a velocity ratio of 4:1 and a maximum velocity of 6. 22 cm/sec. Sidebands are greatly reduced by this method. V)Tracing Distortion Correlator. Fig. 7 shows a blockdiagram of a Tracing Distortion Correlator. This circuit consists of amplifiers, which have a variable amplification factor proportional to 1/R, function generators, differentiators and multipliers. Errors in each block are kept within 1%. Satisfactory results were obtained in hearing tests of disk records produced with this correlator, and the distortion factor of these records were measured to be half that of uncorrected ones. VI)Conclusion This device is useful for the reduction of tracing distortion. A remarkable decrease in secondary distortion is effective especially for stereo disk reproduction. The electronic circuits can be constructed easily.

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Subjective harmaonics are generally interpreted to be caused by the nonlinearity of ears, and seem to have great effects on timbre or tone quality. Wegel and Lane assumed that the intensity of a subjective harmonic could be known by introducing a mistund tone of a slightly different frequency and determing the intensity giving the most pronounced beat sensation. Although this so-called 'Best Beat Method' has been adopted for measuring the intensity of subjective harmonics by many researchers^&lt1), 3), 5), 6)&gt, some objections have been raised against the above-mentioned interpretation^&lt3), 10)&gt. In this paper a P. S. E. Tracing Method developed by the authors is introduced, and the results of experiments are discussed on the sound pressure level and phase of subjective harmonics, monaural phase effect on timble, the phase rule, and a subjective pure tone synthesis. Both soud pressure level and phase of subjective harmonics were measured simultaneously, by adopting the P. S. E. Tracing Method based on successive pair comparisons. This method is characterized by exploring tones consisting of two reciprocal assisiting tones A_&ltnB&gt(Basic phase) and A_&ltnR&gt(Rsversed phase), and a mistuned the M_n. The frequency of assisting tones is the same as that of the subjective harmonic, while the frequency of M_n is slighily different. The mistuned tone is merely introduced to make beats, which intensify observer's sensitivity in adjusting P. S. E. Theoretical considerations are carried out in Fig. 1 under the assumption that the vector addition law holds good in adding external harmonics (assisting tones) to the subjective harmonics. Fig. 2 gives a block diagram of the equipment. A_&ltnB&gt and A_&ltnR&gt are alternately transferred by an electronic switch with a time sequence shown in Fig. 3. The results of experiments are tabulated in tables 2 and 3. Experimental vector loci obtained by this method are shown in Fig. 4, 5 and 6. The agreement of the experimental loci with ones determined theoretically is satisfactory, showing the appropriateness of the assumption. In Fig. 7. comparisons between the results by the Best Beat Method and by the P. S. E. Tracing Method are depicted. The conclusions reached are as follows: (1) The subjective harmonics measured by the new method were approximately 20 dB lower than those by the Best Beat Method. The second subjective harmonic of a fundamental (440 cps. 80 dB SPL), for example, was 46 dB SPL eqe. with a sine phase angle of 262°, while it was 63 dB SPL according to Fletcher. (2) The vector addition law holds good in adding external harmonics to subjective harmonics. (3) The M. P. E. (Monaural Phase Effect) depends largely on subjective harmonics. (4) By adjusting the intensity and phase of external harmonics, observers can hear subjective pure tones. (5) The above-mentioned suggest a hypothesis that the M. P. E. shows itself eventually in the form of a change in amplitude of harmonics due to interactions with subjective harmonics. The phase rule seems to be less reliable with nonlinear actual ears.

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As shown in the previous paper, the bivariate joint probability density destribution P(E_1, E_2) of random noise can be generally expressed in the form of statistical Laguerre's orthonormal expansion series (cf. Eqs. (1) and (2)), where individual characteristics in the statistical properties of random noise (e. g. , the usual linear correlation and the general correlations of high order between two random noise variables) are reflected in four parameters m, s, m_2, s_2, and the expansion coefficients B(n_1, n_2) of joint probability density distribution. Letting m_1=m_2=m and using Eq. (3), the expansion expression of joint moment &ltE^(l_1)_1, E^(l_2)_2)&gt(l_1, l_2=1, 2) and the expansion coefficient B(n_1, n_2)(n_1, n_2=1, 2) are derived from Eq. (1) in a concrete manner by referring to Eqs. (7), (8), (9), (13), (14), and (15). However, for the purpose of putting the theory to practical use, we had better find an approximate expression of the bivariate joint probability density distribution in the closed form instead of using Eq. (1). Thus, we can derive an explicit expression of joint gamma probability distributions (31) and (32) in the closed form as a solution of the integral equation (18). Under the conditions (37), (38) and (39), a general expansion expression (1) in the form of statistical Laguerre's series can be approximated by Eqs. (31) and (32) in the closed form. The conditional probability density distribution of Bessel type derived from Eq. (32) can be rewritten in terms of Eqs. (47) and (48). Finally, the frequency distribution calculated from instantaneous readings of a soundlevel meter recorded at every five seconds (cf. JIS Z 8731) is shown in Fig. 2. And detailed experimental considerations of street noise enough to corroborate the above theoretical results are given in the following two cases:(a)the conditions (37), (38) and (39) for the possibility of approximating Eq. (1) to the closed form (32) (cf. Table 1). (b)the conditional probability density distribution of Bessel type in the form of Eqs. (47) and (48) (cf. Fig. 3).

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