Why can I listen to my mobile phone's radio clearly inside the bus, inside the train, but not inside the elevator? Also, there is an interference of radio signal when the train is accelerating or decelerating. What is the reason behind this?
Electromagnetism – Understanding the Limit of Radio Wave Penetration
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This is something we must all have observed, but I don't know of any definitive study. In the absence of hard data I can think of three potentially relevant effects:
Dielectrics, like the human body, deform electromagnetic fields in their vicinity
The wavelength of FM radio is around 3m and therefore comparable to the size of a typical human. This means your body may be refracting the radio waves.
The proximity of your body may be causing changes in the inductance of coils in your radio and therefore changing the tuning.
Re suggestion 3, I have noticed that with my old radio if I put my arm near it the station fades out but can be retuned. Then when I remove my arm the station fades and needs tuning back to the original setting. This suggests option 3 is the cause, but whether this applies to all radios or just this specific case I don't know.
Whatever the cause, I don't think it's your body generating interference. You lose the signal either because the presence of your body reduces the radio signal strength or in option 3 changes the tuning.
From a physics perspective, the fundamental reason for this is something called the bandwidth theorem (and also the Fourier limit, bandwidth limit, and even the Heisenberg uncertainty principle). In essence, it says that the bandwidth $\Delta\omega$ of a pulse of signal and its duration $\Delta t$ are related: $$ \Delta\omega\,\Delta t\gtrsim 2\pi. $$ A signal with a limited time duration needs more than one frequency to be realizable. (Conversely, you need infinite time to confirm that a signal really is monochromatic.) The bandwidth theorem, which can be proved rigorously for reasonable definitions of the bandwidth and the duration, means that the smaller the time duration is, the larger the bandwidth it requires. It is a direct consequence of a basic fact of Fourier transforms, which is that shorter pulses will have broader support in frequency space.
(This last statement is easy to see. If you have a signal $f(t)$ and you make it longer by a factor $a>1$, so your new signal is $g(t)=f(t/a)$, the new signal's transform is now $$ \tilde g(\omega) =\int g(t)e^{i\omega t}\text dt =\int f(t/a)e^{i\omega t}\text dt =a\int f(\tau)e^{ia\omega \tau}\text d\tau =a\tilde f(a\omega), $$ and this now scales the other way, so it's narrower in frequency space.)
More intuitively, the theorem says that it's impossible to have a very short note with a clearly defined pitch. If you try to play a central A, at 440 Hz, for less than, say, 10 milliseconds, then you won't have enough periods to really lock in on the frequency, and what you hear is a broader range of notes.
Suppose your communications protocol consists of sending pulses of light down a fibre, with a fixed time interval $T$ between them, in such a way that sending a pulse means '1' and not sending it means '0'. The rate at which you can transmit information is essentially given by the pulse separation $T$, which you want to be as short as possible. However, you don't want this to be shorter than the duration $\Delta t$ of each pulse, or else the pulses may start triggering the detection of neighbouring pulses. Thus, to increase the capacity of the fibre, you need to use shorter pulses, and this requires a higher bandwidth.
Now, this is probably very much a physics perspective, and the communications protocols used by real-world fibres and radio links are much more complex. Nevertheless, this limitation will always be there, because there will always be an inverse relation between the width of a signal on the frequency and the time domains.
Best Answer
Buses and trains have lots of glass windows, and radio waves will get through glass. An elevator is effectively a metal box and radio waves can't get through metal.
Have a look at the Wikipedia article on Faraday cages. Any metal enclosure, like an elevator, forms a Faraday cage. The wavelength used by mobile phones is 17cm or 33cm depending on the band, so any window of this size or larger will allow the signal through, but windows significantly smaller than this will block the signal.