Wave Speed & Frequency: Can Bob Tell?

[DiracPool]

I had a thought experiment related to wave speed and frequency.

Lets say we had a wave emitter that emitted transverse plane waves at a regular frequency. Of course we could imagine this as a radio tower, but I wanted it the thought experiment to be more general. Say the emitter is sending out the waves at a frequency of 100 cycles per second (cps). We'll set the wavelength to one meter and we'll set the medium of propagation to one whereby the velocity of the wave in this scenario is 100 m/s.

So what we have is velocity=wavelength x frequency which equals 100=(1)(100)

Now we have an observer Bob watch these waves come in at 100 cps and he gets comfortable seeing this steady, predictable display. After a while, though, we switch the medium between the emitter and Bob so that the speed of the wave is cut in half, down to 50 m/s. Subsequently, Bob now sees the waves coming in at 50 cps.

My question is, is there any way Bob can tell that the wave has slowed down rather than the emitter instead just slowed down it's rate of emission? In other words, can Bob tell that speed of the wave has halved rather than the wavelength of the wave has doubled? Sure, he could ask the emitter tower to stop transmitting, wait a while, and then send a pulse and measure the speed of the pulse, but this thought experiment assumes that this is not possible, all there is a continuously oscillating wave moving through Bob's vicinity.

Part B of the question is the extrapolation to light. I understand that light travels at the constant speed of c in all instances, and that this speed has been measured directly without regard to doppler shift. My question, though, is that, without those direct measurements and Maxwell's equations, etc., if we just had to rely on directly measuring a continuously emitting light source, is there any property inherent in that signal that would allow us to distinguish the velocity from the wavelength/frequency?

 

[harrylin]

I had a thought experiment related to wave speed and frequency.

Lets say we had a wave emitter that emitted transverse plane waves at a regular frequency. Of course we could imagine this as a radio tower, but I wanted it the thought experiment to be more general. Say the emitter is sending out the waves at a frequency of 100 cycles per second (cps). We'll set the wavelength to one meter and we'll set the medium of propagation to one whereby the velocity of the wave in this scenario is 100 m/s.

So what we have is velocity=wavelength x frequency which equals 100=(1)(100)

Now we have an observer Bob watch these waves come in at 100 cps and he gets comfortable seeing this steady, predictable display. After a while, though, we switch the medium between the emitter and Bob so that the speed of the wave is cut in half, down to 50 m/s. Subsequently, Bob now sees the waves coming in at 50 cps.

It's different from what you think. At constant distance, the frequency in steady state is constant; changing the medium changes the wavelength and only has a temporary effect on the received frequency (depending on the speed of switching) as the number of cycles in transit increases. After that, Bob receives the waves again at 100 cps (it's impossible to loose cycles!) and the wavelength is halved.

My question is, is there any way Bob can tell that the wave has slowed down rather than the emitter instead just slowed down it's rate of emission? In other words, can Bob tell that speed of the wave has halved rather than the wavelength of the wave has doubled? Sure, he could ask the emitter tower to stop transmitting, wait a while, and then send a pulse and measure the speed of the pulse, but this thought experiment assumes that this is not possible, all there is a continuously oscillating wave moving through Bob's vicinity.

Without other means of investigation I think that the emitter tower can perfectly simulate the effect of a medium change for Bob. They only have to gradually reduce and then again increase the frequency to the original value. Note that the wavelength in your illustration has halved because the speed has halved.

Part B of the question is the extrapolation to light. I understand that light travels at the constant speed of c in all instances,

According to GR this is only locally the case; non-locally determined the speed of light is reduced in a gravitational field.
- https://en.wikisource.org/wiki/The_...Perihelion-motion_of_the_paths_of_the_Planets.

and that this speed has been measured directly without regard to doppler shift. My question, though, is that, without those direct measurements and Maxwell's equations, etc., if we just had to rely on directly measuring a continuously emitting light source, is there any property inherent in that signal that would allow us to distinguish the velocity from the wavelength/frequency?

In steady state the frequency does not depend on the velocity.