Doppler effect star and earth question

[valueduser]

Hello I have a question that is giving me trouble:

Light of wavelength 659.7 nm is emitted by a star. The wavelength of this light as measured on Earth is 661.1 nm.

How fast is the star moving with respect to Earth? km/s

Is it moving toward Earth or away from it?

Here's where I'm at. I have reasoned that since the wavelength is increasing that the star is moving away. My main problem is determining the frequency of the light. I assume that I can use the formula:

velocity = wavelength * frequency

however the frequency I get just seems wrong. The units are throwing me off too, any help would be greatly appreciated.

 

[berkeman]

What is the equation for the change in frequency of a wave based on its speed and the speed of the emitter? And keep in mind that the speed of light is about 300*10^6m/s (check this before using it, though), so that gives you a way to convert between frequency and wavelength.


EDIT -- Fixed typo in speed of light. It's 300*10^6, not *10^8. Sorry.

 

[kyle8921]

Hello there,

The Doppler effect is a phenomenon that occurs when there is relative motion between a source of waves (in this case, the star) and an observer (Earth). When the source is moving towards the observer, the wavelength of the waves appears shorter, resulting in a higher frequency. Conversely, when the source is moving away, the wavelength appears longer and the frequency decreases.

In this scenario, we know that the observed wavelength of the light is longer than the emitted wavelength, which means the star is moving away from Earth. To determine its speed, we can use the formula you mentioned: velocity = wavelength * frequency. However, we need to first find the frequency of the light.

To do this, we can use the relationship between frequency and wavelength: frequency = speed of light / wavelength. The speed of light is a constant value of 3*10^8 m/s. Converting the given wavelengths to meters (659.7 nm = 6.597*10^-7 m and 661.1 nm = 6.611*10^-7 m), we can plug these values into the formula to get the frequency of the emitted light as 4.553*10^14 Hz.

Now, we can use the formula velocity = wavelength * frequency to find the speed of the star. Plugging in the values for the observed wavelength (6.611*10^-7 m) and the calculated frequency (4.553*10^14 Hz), we get a speed of 2.999*10^5 m/s or approximately 299.9 km/s.

In summary, the star is moving away from Earth at a speed of 299.9 km/s. I hope this helps clarify any confusion you had. Keep in mind that the Doppler effect can also be observed in other types of waves, such as sound waves, and is an important concept in many fields of science. Keep exploring and learning!