(9) = Lw - 20log= - 10 log(4n) Ly = 10109 Iref = 10109 Was.4urz where r is a reference distance that is introduced to nondimensionalize the argument of the log.4.2 Pre-lab question Using the material provided in the background section, plot the transmission loss (TL), in dB, as a function of distance (d) between a receiver and a hemispherical sounds source. Set the transmission loss at zero for d = 0. It should then increase progressively at a function of d, due to wave divergence. 2.2.2 Relative measures The measures discussed so far are absolute ones in the sense that are directly related to physical characteristics of sound. These measures are not very informative with respect to human perception since the reaction to a given frequency is subjective, and hence a frame of reference of sound perception is absent. Furthermore, the range between silence, or the threshold of hearing, and sound power that would cause pain is very large. The power for the threshold of pain iz about 32 x 10*? that of the threshold of hearing. In order to deal with this problem, the threshold of hearing at 1 kHz is used as reference. This corresponds to a pressure of 2 % 10 Pa, or a power density (intensity) of 1077 Watts m~ The problem of representing a large range of values is addressed by adopting a logarithmic scale. The Sound Intensity Level L the Sound Pressure Level L., and the Sound Power Level L, are introduced to represent relative measures of sound. Sound intensity level: The sound intensity level Lr compares the sound intensity to the standard adopted to represent silence in a logarithmic scale. It iz defined by I L;=10log, (6) ref where [, = 107 Watts m~. Logarithms are in base 10. Sound Pressure Level: At a distance large enough from the sound source, the sound wave front appears to a recetver to be planar, and the relationship between the sound intensity 7 and the sound pressure P is given by Equation (5). Substitution for J from Equation (3) into Equation (6] gives 3 I = P L= = 20log =, (7 ref Ea o 4 in o where P,.=2 x 107 Pa. Sound power level: The sound power level compares the relative magnitude of the prevailing sound power to the sound power that cannot be perceived, and it is defined by W Ly = 1logm (8) Where Wi =107 Watts. The relationship between the Lr and Ip can be derived by substituting I into Equation (8) based on the appropriate sound wave propagation pattern to be modelled. For a spherical wave propagation the following relationship results from Equation (23 the partition separating them is removed, such that we can assume TL=0 in Eq. (13). By measuring the microphone voltage response as a function of frequency we obtain the following baseline normalization spectrum B(D): S;(f ) V.(f) B(f) = 20 108 5. (f ) 20 108 V.(f )| 71=0 (14) Once this normalization spectrum is measured, it can be used for all partitions to calculate their transmission loss spectra TL(f) as a function of microphone voltages using: TL(f) = 20 108 v.(f ) B (f ) (15)Root Mean Square (RMS) value P is used to indicate the amplitude. This is calculated as follows: (1 Ml where P and P have the physical dimensions of pressure. Sound Intensity: The sound intensity J is an absolute measure, calculated as the ratio of the power emitted 17" over the area over which the wave front iz dispersed. Omnidirectional sound, like that emanating from a tuning fork, propagates in a spherical pattern, hence the intensity [ at a given radius from a point source iz given by W @ 4y Sound emanating from a loud speaker is directional. The majority of the power emitted by the loud speaker is directed according to a specific orientation. The waves propagate forward in 2 semi-spherical front, hence for a point source the intensitv at a given radius 15 given by B W T 2t (3) This 15 an idealized case where the diaphragm of the loud speaker is flat and is flush with the loud speaker front plane. At a relatively close proximity to a linear sound source like a traveling train or a vibrating string, sound propagates in the form of an expanding cvlinder with its axis aligned with the source. The intensity in this case is given by W | =0o 4 2mrd ) where 4 iz the length of the linear source. Sound emanating from the extremity of a pipe will not lose itz intensity as it travels down the pipe since the area along the path iz constant. Sound pressure: The relationship between sound intensity and sound pressure is given by 2 _F = (5) wherte pis the density of the medium and - is the speed of sound in the medium. This relation 15 valid for waves propagating with parallel wavefronts. At a relatively far distance from a sound source, the wave front appears flat with respect to a sound receiver. Sound lab - page 3 Sound absorption: Sound absorbers convert some of the sound energy impinging on them into heat. If the walls of the large hall mentioned above is lined with sound absorbing material. sound waves would not reverberate in it. Walls of concert halls are commonly lined with sound absorbing panels to improve their acoustic qualities. The absorption quality of a material is defined by its Absorption Coefficient. A material with absorption coefficient equal to zero reflects sound waves with no attenuateon in its level. A material with absorption coefficient equal to one absorbs all the sound waves impinging on it. Transmission coefficient: When sound waves impinge on a partition the related pressure waves cause the partition to vibrate, generating a sound pressure wave that emanates from the other side of the partition. The sound intensity emanating from the partition may be less than that impinging on the partition. The difference is the sound energy that the partition absorbed. The transmission coefficient a is defined as the ratio of the sound intensity transmitted through the partition, It, to that impinging on the partition, It and it is expressed as a = It (10) Transmission loss: The intensity of sound transmitted through a partition depends on the frequency and the angle of incidence of the sound wave. The transmission loss IZ is the reciprocal of the transmission coefficient in decibel and is given by TL = 10 log , -10 log a (11) Measurement with microphones: The intensity of incident and transmitted sound waves can be measured, as in the present experiment, using two microphones that are positioned on each side of the partition under test. These microphones convert the pressure wave amplitudes (P:, P.) to a readout voltage (Vi, V, ) with sensitivities S;, S, (in V Pal): (12a) V. = S.P (12b) In this case, the transmission loss expression becomes: PF TL = 10 log 10109 pz = 20 10g V,St V:Si = 20108 V. Vi _ 20108 5. Si (13) Microphone normalization: If microphone sensitivities S; and S, are equal at all frequencies of interest, the last term in the above equation cancels out, such that measuring microphone voltages directly is sufficient to obtain TZ for any given partition. However, this situation rarely occurs, and characterizing the microphone sensitivity ratio in a separate experiment is usually necessary. To do so, the microphones are brought close together and