College Physics II – Mechanics, Sound, Oscillations, and Waves
Definition
$f_s$ is the frequency of the sound source in the Doppler effect, which is the apparent change in the frequency of a wave (or other periodic event) for an observer moving relative to the source of the waves. The Doppler effect is observed with all types of waves, including sound waves, light waves, and radio waves.
congrats on reading the definition of $f_s$. now let's actually learn it.
The Doppler effect causes the observed frequency ($f_o$) to be higher than the source frequency ($f_s$) when the observer is moving towards the source, and lower than $f_s$ when the observer is moving away from the source.
The Doppler shift is proportional to the relative velocity between the observer and the source, and the direction of the shift depends on whether the observer is moving towards or away from the source.
The Doppler effect has many practical applications, such as in radar guns used by police to measure the speed of vehicles, and in the detection of exoplanets (planets orbiting other stars) through the observation of their Doppler-shifted spectra.
The Doppler effect is also observed for light waves, leading to the cosmological red shift, which is evidence for the expansion of the universe.
The mathematical formula relating the observed frequency ($f_o$), the source frequency ($f_s$), and the relative velocity ($v$) is: $f_o = f_s * (1 + v/c)$, where $c$ is the speed of the wave (e.g., the speed of sound or the speed of light).
Review Questions
Explain how the Doppler effect relates to the frequency of the sound source ($f_s$).
The Doppler effect is the apparent change in the frequency of a wave, such as a sound wave, due to the relative motion between the source of the wave and the observer. The frequency of the sound source, $f_s$, is a key parameter in the Doppler effect. When the observer is moving relative to the source, the observed frequency, $f_o$, will be different from the source frequency, $f_s$, due to the Doppler shift. The magnitude and direction of the Doppler shift depend on the relative velocity between the observer and the source, as well as whether the observer is moving towards or away from the source.
Describe how the Doppler effect can be used to detect the motion of celestial objects, such as exoplanets.
The Doppler effect can be used to detect the motion of celestial objects, such as exoplanets, by observing the shift in the frequency of the light emitted by these objects. As an exoplanet orbits its host star, the relative motion between the planet and the Earth causes a Doppler shift in the light emitted by the planet. By measuring the periodic Doppler shift in the spectrum of the host star, astronomers can infer the presence and properties of the orbiting exoplanet, including its mass and the size of its orbit. This technique, known as the radial velocity method, has been instrumental in the discovery of thousands of exoplanets.
Analyze the mathematical relationship between the source frequency ($f_s$), the observed frequency ($f_o$), and the relative velocity ($v$) in the context of the Doppler effect, and explain how this relationship can be used to calculate the relative speed of a moving object.
The mathematical relationship between the source frequency ($f_s$), the observed frequency ($f_o$), and the relative velocity ($v$) in the context of the Doppler effect is given by the formula: $f_o = f_s * (1 + v/c)$, where $c$ is the speed of the wave (e.g., the speed of sound or the speed of light). This formula can be rearranged to solve for the relative velocity $v$, which is given by $v = c * (f_o/f_s - 1)$. By measuring the source frequency $f_s$ and the observed frequency $f_o$, and knowing the speed of the wave $c$, one can calculate the relative velocity $v$ between the observer and the source. This relationship is the basis for many practical applications of the Doppler effect, such as the use of radar guns by law enforcement to measure the speed of moving vehicles.
Related terms
Doppler Shift: The change in frequency of a wave for an observer moving relative to the source of the wave. This is the underlying phenomenon behind the Doppler effect.
Observed Frequency ($f_o$): The frequency of the wave as observed by a moving observer, which is different from the frequency of the source ($f_s$) due to the Doppler effect.
Relative Velocity ($v$): The velocity of the observer relative to the source, which determines the magnitude of the Doppler shift.