# Why doesn't the motion of a car affect the frequency of radio stations?

When we go in a car and tune to an FM radio station, why doesn't our motion disturb the frequency? Like the Doppler effect?

• See also Why don't interfering radio stations both play at the same time? (the questions are only mildly related, but they're both questions I had when I was learning how radios work, so I thought you'd find it interesting as well) – BlueRaja - Danny Pflughoeft Jun 3 '15 at 16:37
• @DARU SRINIVAS One interesting point to consider would be the effects on higher-frequency radios, such as ones used for cellular telephony (Say 1.9 GHz/2.1 GHz LTE) or L-band Digital Audio Broadcast at around 1,4 GHz. – AndrejaKo Jun 3 '15 at 22:23
• It might have been better to ask about AM rather than FM although I expect the answer is still "the difference is so small as to not matter at terrestrial speeds". – CJ Dennis Jun 4 '15 at 6:27
• It does, but the amount is insignificant for FM radio - more sensitive protocols e.g. 4G/LTE cellular data transmissions have special treatment to correct for that and still lose some bandwitdh if the phone is rapidly moving. – Peteris Jun 4 '15 at 6:35
• @CJDennis AM is generally more sensitive to correct tuning than FM, but 10Hz off center is still not a big deal. And since broadcast AM is medium-wave (about 100 times lower frequency than broadcast FM), the resulting Doppler is also 100 times smaller, i.e. less than 1Hz. – hobbs Jun 4 '15 at 21:08

It does! However it doesn't change the frequency enough to matter.

An FM transmission is not a precise frequency. Instead it spans a range of about 100 or 200 kHz depending on which country you are in. So your FM radio actually accepts a range of frequencies either side of the central frequency.

Let's suppose you're travelling at the maximum speed permitted in the UK, which is 70 mph or just over 30 m/s. This will Doppler shift the frequency of the FM station by a factor of about 1.0000001. In the UK the FM frequency is around 100 MHz, so the shift in frequency is about 10 Hz. This is only 0.01 % of the range of frequencies the transmission uses, so the frequency shift does not affect reception.

To seriously affect reception you'd need to be travelling at around 100 000 miles per hour.

For completeness I should probably add that modern radios auto tune, and would automatically compensate for a change of frequency due to the Doppler shift.

• The channel separation used is less than the bandwidth required for a transmission - geographically close transmitters are not allocated adjacent channels, but typically separated by at least 500 kHz. – Floris Jun 3 '15 at 13:21
• The TDA9809M PLL chip commonly used in FM radios has a capture range of 1.4 MHz - you would have to travel at more than 1% of the speed of light to give it trouble with finding the station... That's about 7 million mph, quite a bit more than you estimated. – Floris Jun 3 '15 at 16:22
• With frequency modulated signal, wouldn't the Doppler shift (assuming you're going sufficiently fast) warp the signal before interfering with reception? – Superbest Jun 4 '15 at 0:45
• I deleted a few amusing but ultimately off-topic comments. – David Z Jun 5 '15 at 12:50
• @Superbest: With FM modulation, a frequency shift would (to a first approximation) just lead to an DC offset of the demodulated signal. Even if the receiver doesn't adjust its tuning automatically, this is unlikely to survive the audio amplifier stages, and can't be heard even if it does. No audible warping. – Henning Makholm Jun 5 '15 at 16:23

To further add to John Rennie's answer: you don't even need autotuning for a frequency drift of the magnitude John calculates (10Hz): all FM receivers I've ever dealt with (I qualified as an electrical engineer in 1985 and worked a few short years in communications before returning to study) demodulated with a phase locked loop detector, whose job it is to follow drifts in the carrier frequency like this.

In any case, in any FM demodulation, a constant 10Hz offset decodes to a very small DC (*i.e.zero hertz constant offset) signal: let's say the full dynamic range corresponds to $10^5Hz$ as in John's answer, this offset is 80dB down on the demodulator's full dynamic range. The fully demodulated signal probably doesn't reproduce signals down to DC anyway. Your car's speed cannot change quickly, so variations in its speed would correspond to a variation in this offset with a frequency of a hertz or so maximum: if it gets through the full demodulation filter at all, it's going to have negligible effect on the signal.

John and Rod already pointed out that the expected frequency shift from driving a car is "small"; I would like to expand a little more on the way FM works.

FM = Frequency Modulation. The carrier (nominal center frequency) is being modulated - that is, in order to convey the audio content, the frequency is actually moving around deliberately in order to get the music into your car. And it moves quite a lot.

In the case of FM, you have to worry about two things in the modulation:

1. What is the relationship between amplitude range you want to convey, and the frequency shift?
2. What is the highest frequency you want to transmit?

Some of the following facts were taken from this presentation.

The frequency response is typically 50 Hz to 15 kHz; 100% modulation is defined as 75 kHz on either side (max amplitude). For stereo FM, the highest modulating frequency is 53 kHz. According to Carson's Rule, the minimum channel width should be $CBR = 2(\Delta f + f_m)$ where $CBR$ is the bandwidth requirement, $\Delta f$ is the frequency swing corresponding to full amplitude, and $f_m$ is the maximum modulation frequency (53 kHz). This means that an FM transmitter needs 256 kHz according to this rule - reason why geographically close transmitters are never next to each other on the dial (channels are allocated on 200 kHz slots, but you can't transmit at 90.1 and 90.3 in the same town and get away with it).

Driving at a constant speed will not affect your reception - the PLL in the receiver has no problem locking in to a signal that is significantly off the target frequency (much more than the shift you can get from car motion - accounting for all other sources of drift in transmitter and receiver, and for the fact that the modulated signal varies by 256 kHz).

You might wonder: if you attached your antenna to a wheel that is spinning very rapidly, would you be able to hear a low frequency hum as you add a small modulation of the carrier? Your wheel would have to turn at about 3000 rpm (to give a 50 Hz signal); and if the full amplitude if 75 kHz (corresponding to e.g. 80 dB on your speakers) and your threshold of hearing is 40 dB (really it is lower, but with a spinning wheel nearby you'd be hard pressed...) you can hear an amplitude that is 100x smaller - which would require a peak shift of 750 Hz and thus a velocity of $3\cdot 10^6 \mathrm{m/s}$. At 50 Hz (300 rad/sec to keep round numbers) you would need a wheel that is 10 km in radius.