A linear model for wave attenuation is presented, where Q, the energy loss per cycle, is exactly independent of frequency. Wave propagation is fully described by two parameters: Q and a phase velocity at an arbitrary reference frequency. An exact derivation leads to a phase velocity expression as a function of frequency. Scaling relationships for pulse propagation are derived, showing that pulse risetime or width is proportional to travel time. For a delta function source, travel time is proportional to $ x^d $, where $ \beta = 1/(1 - \gamma) $. The constant Q theory fits both data sets from field observations in the Pierre shale formation, interpreted by Ricker and McDonal et al. The constant Q model is simpler than nearly constant Q (NCQ) models and is mathematically defined by two parameters: phase velocity at a reference frequency and Q. Unlike NCQ models, which focus on the frequency domain, the constant Q model allows for exact analytical expressions for various frequency domain properties, valid over any frequency range. The paper emphasizes time domain descriptions, providing exact expressions for creep and relaxation functions and scaling relations for transient wave pulses. Approximate expressions for impulse responses are also given. The constant Q model shows that when the frequency range is restricted and losses are small, results from NCQ theories approach those from the constant Q model. The paper discusses the time domain representation of wave propagation, showing that the velocity dispersion associated with anelasticity may be more clearly observed in the time domain than in the frequency domain. Strick's steepest descent approximation provides a good time domain representation for the impulse response. The constant Q model is applied to field observations from the Pierre shale formation, showing that it fits both data sets interpreted by Ricker and McDonal et al. The model's scaling relations are used to analyze pulse propagation, showing that travel time, pulse width, and pulse amplitude are related by $ T \propto \tau \propto 1/A \propto (x/c_0)^\beta $. The paper also discusses the implications of these scaling relations for wave propagation in different materials. The constant Q model is compared with NCQ theories, showing that while NCQ models are more complex, the constant Q model provides a simpler and more accurate description of wave propagation in real materials. The paper concludes that the constant Q model is a valid and practical description of wave propagation and attenuation, with Q being weakly dependent on frequency. The model is shown to be consistent with field observations and laboratory experiments, and it is suggested that the constant Q model is more appropriate for describing wave propagation in real materials than NCQ models.A linear model for wave attenuation is presented, where Q, the energy loss per cycle, is exactly independent of frequency. Wave propagation is fully described by two parameters: Q and a phase velocity at an arbitrary reference frequency. An exact derivation leads to a phase velocity expression as a function of frequency. Scaling relationships for pulse propagation are derived, showing that pulse risetime or width is proportional to travel time. For a delta function source, travel time is proportional to $ x^d $, where $ \beta = 1/(1 - \gamma) $. The constant Q theory fits both data sets from field observations in the Pierre shale formation, interpreted by Ricker and McDonal et al. The constant Q model is simpler than nearly constant Q (NCQ) models and is mathematically defined by two parameters: phase velocity at a reference frequency and Q. Unlike NCQ models, which focus on the frequency domain, the constant Q model allows for exact analytical expressions for various frequency domain properties, valid over any frequency range. The paper emphasizes time domain descriptions, providing exact expressions for creep and relaxation functions and scaling relations for transient wave pulses. Approximate expressions for impulse responses are also given. The constant Q model shows that when the frequency range is restricted and losses are small, results from NCQ theories approach those from the constant Q model. The paper discusses the time domain representation of wave propagation, showing that the velocity dispersion associated with anelasticity may be more clearly observed in the time domain than in the frequency domain. Strick's steepest descent approximation provides a good time domain representation for the impulse response. The constant Q model is applied to field observations from the Pierre shale formation, showing that it fits both data sets interpreted by Ricker and McDonal et al. The model's scaling relations are used to analyze pulse propagation, showing that travel time, pulse width, and pulse amplitude are related by $ T \propto \tau \propto 1/A \propto (x/c_0)^\beta $. The paper also discusses the implications of these scaling relations for wave propagation in different materials. The constant Q model is compared with NCQ theories, showing that while NCQ models are more complex, the constant Q model provides a simpler and more accurate description of wave propagation in real materials. The paper concludes that the constant Q model is a valid and practical description of wave propagation and attenuation, with Q being weakly dependent on frequency. The model is shown to be consistent with field observations and laboratory experiments, and it is suggested that the constant Q model is more appropriate for describing wave propagation in real materials than NCQ models.