Frequency shift refers to the change in the observed frequency of a wave due to the relative motion between the source of the wave and the observer. This phenomenon is known as the Doppler effect and is also observed in the context of sonic booms.
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The frequency shift observed in the Doppler effect is proportional to the relative velocity between the source and the observer.
For a source moving towards the observer, the observed frequency is higher than the emitted frequency, resulting in a blueshift.
For a source moving away from the observer, the observed frequency is lower than the emitted frequency, resulting in a redshift.
Sonic booms are caused by the sudden change in air pressure as an object moves through the air at supersonic speeds, creating a frequency shift in the sound waves.
The magnitude of the frequency shift in the Doppler effect and sonic booms can be used to calculate the relative velocity between the source and the observer.
Review Questions
Explain how the Doppler effect relates to the concept of frequency shift.
The Doppler effect is the underlying phenomenon that causes a frequency shift. When a source of waves, such as sound or light, is moving relative to an observer, the observed frequency of the waves will be different from the emitted frequency. If the source is moving towards the observer, the observed frequency will be higher (a blueshift), and if the source is moving away, the observed frequency will be lower (a redshift). This change in observed frequency is known as the frequency shift, and it is a direct consequence of the Doppler effect.
Describe the relationship between frequency shift and the creation of sonic booms.
Sonic booms are caused by the sudden change in air pressure as an object moves through the air at supersonic speeds, which is greater than the speed of sound. This sudden change in air pressure creates a frequency shift in the sound waves, resulting in the characteristic loud, explosive sound of a sonic boom. The magnitude of the frequency shift is directly related to the velocity of the object relative to the speed of sound, with a larger frequency shift occurring at higher supersonic speeds. Understanding the frequency shift associated with sonic booms is crucial for predicting and mitigating the effects of these disturbances.
Analyze how the frequency shift observed in the Doppler effect and sonic booms can be used to calculate the relative velocity between the source and the observer.
$$f_\text{observed} = f_\text{emitted} \left( \frac{c \pm v_\text{source}}{c \pm v_\text{observer}} \right)$$ Where $$f_\text{observed}$$ is the observed frequency, $$f_\text{emitted}$$ is the emitted frequency, $$c$$ is the speed of the wave (e.g., speed of sound or speed of light), $$v_\text{source}$$ is the velocity of the source, and $$v_\text{observer}$$ is the velocity of the observer. By measuring the frequency shift and knowing the speed of the wave, you can rearrange this equation to solve for the relative velocity between the source and the observer. This relationship is crucial for applications such as determining the speed of moving objects, measuring the expansion of the universe, and understanding the behavior of supersonic aircraft.
The Doppler effect is the change in the observed frequency of a wave, such as sound or light, due to the relative motion between the source and the observer.