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MSU PHY 252 - Speaker

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1 THE SPEAKER OBJECTIVES: 1) Know the definition of "decibel" as a measure of sound intensity or power level. 2) Know the relationship between voltage and power level measured in decibels. 3) Illustrate how the performance of an audio speaker is rated. 4) With the input voltage to a speaker held constant, measure the output voltage from a microphone at various frequencies. Plot the speaker response (in decibels) vs. frequency. INTRODUCTION: Because almost all uses of sound involve the human ear, a special scale, called the decibel (dB), is widely used to measure the sound intensity. The decibel scale roughly corresponds to the sensation that a human ear experiences when a sound strikes it. The decibel scale is related to the physical sound intensity measured in watts/cm2 by the following equation: I = 10 log PPR defines I in units of decibels (dB) (1) where, P is the sound intensity measured in watts/cm2, PR is a reference sound intensity (also in watts/cm2), and log is the logarithm to the base 10. We will usually put the (dB) in such equations in parentheses to remind us that it is a unit, not a factor in the formula. From equation (1), it can be seen that the decibel scale is a measure of the relative intensity of two sound levels. Example: P = 10-2 W/cm2 PR = 10-6 W/cm2 The factor of "10" is in the decibel equation because the resulting decibel unit represents approximately the smallest increment in sound level that is noticeable to a human ear. Without the factor of 10, the intensity I would be in bel units, which are too large to be convenient. Given a value for I, we can solve for the ratio P/PR by using the fact that 10x is the inverse of log x. From equation (1), if I=1 dB, we have P/PR=100.1=1.26. Thus, a 26% change of power level (in watts/cm2) is just barely detectable by a human ear. The decibel scale is defined in terms of ratios, so one must choose a reference, PR. No matter what PR is chosen, that power level by definition represents 0 dB since: logPRPR      = 0 dB)(404101010101010 I462=×===−−log logIntroductory Physics Experiments (Physics 252) 2 This does not cause serious ambiguity. Suppose we changed our mind about the reference in equation (1) and used QR instead. What happens? Inew = 10 log PQR = 10 log ×RRRQPPP = RPPlog*10 + RRQPlog*10 = I + constant The constant has to do only with the ratio of the old and new reference levels. So changing reference values does not change the shape of the curve of I values (vs. frequency, for example), but merely shifts the origin. For most of this experiment, we will use for the reference power the power at a specific frequency, 2000 Hz. In work with sound levels and the human ear, the value 10-16 watts/cm2 is normally used because it is about the weakest sound intensity detectable by a human ear. For a sound intensity of P=PR, the decibel intensity is 0 dB, since log PRPR      = 0 A very loud sound can cause pain to a human ear. The highest sound intensity that a human ear can tolerate without experiencing pain is about 10-4 watts/cm2, which is 10 * log 10−410−16 = 10 * log 1012 = 10 x 12 = 120 (dB) The ear is a remarkable sound detector. It can detect sound intensities over a range of 12 decades in decibels! The decibel difference between two sound intensities P1 and P2 (in watts/cm2) is given by: −=−=∆RRPPlogPPlogIII1212*10*10 Or: The following table gives some useful numbers: power ratio P2/P1 decibel difference (dB) 1.26 1.00 2 3.01 10 10.00 20 13.01 )dB(*1012=∆PPlogIThe Speaker (Version 4.0, 1/7/2002) 3 100 20.00 1000 30.00Introductory Physics Experiments (Physics 252) 4 The sound level in W/cm2 produced by an audio speaker is directly proportional to the electrical power in W provided as input to the speaker. Therefore, the input power to a speaker is also often measured in decibels. Since it is often easier to measure the voltage in an electrical circuit, it is desirable to know the relationship between the electrical power in decibels and the voltage ratio. For a resistive load, we have P =V2R Here P is the power in watts, V is the voltage in volts, and R is the resistance in ohms. If the equivalent resistance in the circuit is a constant, then the power ratio can be written as, P2P1=V22V12 Thus, the power level difference in decibels can be written as, ∆I = 10 logP2P1      =10 logV22V12      = 20 logV2V1      (dB) In audio circuits, the power ratio P2/P1 could represent either an electrical power ratio or a sound intensity ratio. One of the applications of the decibel scale is in the specification of the frequency response of audio equipment (e.g., a speaker or a microphone). There are many measures of the quality of an audio system, one of them being the frequency response. To achieve true reproduction of music or voice, a good audio system should have uniform (constant) sound reproduction efficiency over frequency range from 20 Hz to 20000 Hz. This means, with the input intensity held constant, if one plots the output intensity as a function of frequency, the curve should be flat in this frequency range. Since we are not so concerned about the absolute efficiency here, one often plots the relative efficiency as a function of frequency. The relative efficiency IS as a function of frequency is defined as IS(f) = 20 log ()( )refoutoutfVfV (dB) Here Vout(f) is the output voltage at the frequency f, Vout(fref) is the output voltage at the reference frequency fref. Usually an intermediate frequency, such as 2000 Hz, is chosen as the reference frequency. Good sound reproduction means that the power out of the speakers is directly proportional to the input power (from the recording), no matter what the frequency. For this to be true, the output for a fixed input power also must be constant at any frequency.The Speaker (Version 4.0, 1/7/2002) 5 1 011 021 031 041 05Frequency HzOutput dB10 dB0 REF Frequency Response Curve of a Stereo Phonograph Pickup Cartridge Figure 1 Figure 1 is a graph published in a "hi-fi" magazine indicating the frequency response curve of a particular stereo phonograph cartridge. The upper curve is the output of the


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