To solve this problem we can examine the doppler effect equation:

 where  is the velocity of the observer,  is the velocity of sound through air, vs is the velocity of the source of the sound,  is the original frequency of the source, and is the source's apparent frequency to the observer. Because we are dealing with a stationary observer and a source in motion, we will add the velocity of the source to the velocity of sound. We can then plug in the values given by the problem into the above equation:

The first thing we need to do is convert the wavelengths given to a usable frequency using:

Where  is frequency,  is the speed of light , and  is the wavelength.  Once we have the frequencies, we can find the velocity of the star in regards to Earth:

Plug in known values into the Doppler equation. We may assume the Earth is stationary relative to the star.

Simplify.

We can use the following equation to solve this problem:

where

   v = velocity of sound

   f = frequency

    = wavelength

Rearranging for wavelength, we get:

Plugging in our values, we get:

You do not need to have this equation memorized in order to solve this problem. A very useful skill in physics is being able to solve problems based solely off your units.

We need to have an answer with the units of meters. We are given units of m/s and 1/s. How can we go from these to meters? Simply divide the value with the units of m/s by the value with the units of 1/s. This gives you an answer with the units of meters. Once written out, this is the final equation written above. No need to spend extra time memorizing the equation!

We need to know the speed of light, which is:

We can use this to calculate the wavelength of any electromagnetic wave if we know the frequency, using the equation:

If you're unsure of how to come about this equation, you should be able to derive it by looking at your units. Use our given values to solve for the wavelength:

Since the wave has a frequency of 30Hz, we know it completes 30 cycles every second. As its velocity is , we also know that in that second, the wave has moved 10m. Dividing the total distance, 10m, by the number of cycles, 30, we get the number of meters travelled in each cycle which is the wavelength:

Speed is frequency times wavelength. So the frequency must be speed divided by wavelength. In this case:

This makes sense as in one second, the wave will have travelled 15m. Each meter is 5 cycles, so over the distance the wave has travelled in one second, it has completed  cycles.

A trigonometric equation given by the following formula

Here,  is given in meters,  is given in Hertz,  is given in seconds, and  is given in meters. The period is given by:

In our case:

Radio waves travel at the speed of light . The relationship between wavelength, frequency, and wave speed is

, where  is the wavelength and  is the frequency. 

In our case, 

. 

Therefore,

Amplitude refers to the strength of a wave and has no relation to its frequency. Frequency would only affect the period and phase, but not the amplitude. 

The relationship between wavelength and velocity is given by the equation;

The question gives us the velocity of the wave and its frequency. Using these values, we can solve for the wavelength.