New answers tagged approximations
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Wikipedia states that the relativistic Doppler effect is the same whether it is the source or the receiver that is stationary. Can this be true?
This considers a more general case in which
both the source and the receiver are in motion in the lab frame.
This calculation (using a spacetime diagram and its geometry)
will obtain the Doppler ...
- 12k
16
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Wikipedia states that the relativistic Doppler effect is the same whether it is the source or the receiver that is stationary. Can this be true?
The relativistic Doppler factor has to be the same whether it is the receiver or the source that is considered to be stationary, because in relativity there is no way to determine if it is the ...
- 6,102
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Wikipedia states that the relativistic Doppler effect is the same whether it is the source or the receiver that is stationary. Can this be true?
For sound waves propagating in a medium, there is an obvious absolute frame of in which the sound wave exists with a frequency that does not depend on the motion of the source (Tx) or receiver (Rx).
...
- 35.4k
24
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Accepted
Wikipedia states that the relativistic Doppler effect is the same whether it is the source or the receiver that is stationary. Can this be true?
You have to include a factor of $\gamma$ in both effects. The terms that are the same are $\gamma (1-\frac v c)$ and $\frac 1 {\gamma \left(1 + \frac v c \right)}$. This is because
$\displaystyle \...
- 56.4k
6
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Wikipedia states that the relativistic Doppler effect is the same whether it is the source or the receiver that is stationary. Can this be true?
But your final two expressions are approximately the same in the limit $v\ll c$. Use the binomial expansion,
$$
\begin{align}
(1+\epsilon)^n&= 1+n\epsilon+\frac{n(n-1)}{2!}\epsilon^2+\cdots
\\&...
rob♦
- 91.5k
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The "small amplitude" assumption in the derivation of the wave equation for the string
Following the most recent comment, I am going to try and prove that the “vertical displacement force law” assumption implies the small-amplitude assumption. The small-amplitude assumption is ...
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The "small amplitude" assumption in the derivation of the wave equation for the string
A propos "the restoring force being proportional to the displacement," a textbook that does not use the small-amplitude assumption in the derivation of the wave equation for the string is ...
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David Tong, notes on General Relativity, pg. 25
I was puzzled enough to look at what the notes actually say. You have the quote right though.
I think he starts from
$$
\sqrt{a+x}= {\sqrt a}\sqrt{1+ \frac x a}\\
\approx \sqrt{a}\left(1+ \frac 12 \...
- 54.5k
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What is the justification for $n+\ell$ rule in quantum mechanical model of atom?
I just accidentally came across this question in relation with a more recent almost coincident one, so I will duplicate my answer here, as I believe the answer above does not fully elaborate on the ...
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Precise relation between temperature change and physical quantities
$$ \frac{l_1}{l_2}=\frac{1+\alpha\theta_1}{1+\alpha\theta_2} \implies
> l_2 = l_1\frac{1+\alpha\theta_2}{1+\alpha\theta_1} $$ The equations
above give us two different answers for lengths at a ...
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4
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Accepted
Adiabatic Approximation in the spin 1/2 System
It isn't just the point $t=0$ where the transition rate is strongest, it is the whole region of time where $$|t| \lesssim {\small \frac2\alpha} H_{12} \tag{1}$$
and the reason can indeed be seen ...
- 4,912
1
vote
Accepted
WKB Approximation of the Quasinormal Mode Spectrum of the Poschl-Teller (PT) Potential
Okay so this question was really bugging me so I spent the afternoon learning how to do the approximation.
The general Poschl-Teller Potential is $V(x) = \frac{V_o}{\cosh^2(\alpha \cdot (x-x_0))} $
I ...
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WKB Approximation of the Quasinormal Mode Spectrum of the Poschl-Teller (PT) Potential
Schrödinger operators with reflectionless Pöschl-Teller potentials arise in the study of SUSY chains of one-dimensional non-linear field theories labeled by $N$. The two first members of the family ...
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