The frequency of a wave is directly related to the energy in the wave. The most energetic waves in the electromagnetic spectrum are gamma rays. Gamma rays are typically released from quasars, ultra-dense dying stars, and from atomic bomb blasts, which gives you the scope of the amount of energy involved with gamma rays.

Frequency, when given an equation in sine or cosine notation, is the value inside the parenthesis. For the second harmonic , the frequency is:

The will be destructive interference when 

Using

Plugging in values:

When waves add together and make a larger wave, think of them as constructing a big wave. On the other hand, waves that make a smaller wave are said to be destructive because they are "destructing" each other and making a smaller wave, or no wave at all.

Because light has properties of waves, it can have interference. When two crests of the wave meet, this is known as constructive interference, and results in the two crests adding, meaning the light gets brighter. When a crest and a trough meet, this is known as destructive interference, and results in the two partially or completely cancelling each other out, making the observed light less bright.

This question is describing a scenario in which a ray of monochromatic light is being refracted by passing from air into glass. We're then asked to determine which parameter of the light does not change.

First of all, let's review what refraction is. Refraction is an event that happens whenever light passes from one medium into another medium. In doing so, the ray bends. This bending of light is due to the fact that the speed of light changes depending on the medium in which it is traveling.

As the light crosses from the air and into the glass, its speed is slowed down. This is because glass is denser than air. Also, since the speed of light is a function of both wavelength and frequency, then one or both of these variables must change. The frequency remains unchanged while the wavelength becomes altered. One way to think about this is by applying conservation of energy. If the frequency changed, then the energy of the light would also change. However, the energy of the light remains unchanged during refraction. Thus, only the wavelength and the speed change.

Since frequency remains the same, we also know that the period will stay the same, since period is just the inverse of frequency. Also, as was mentioned above, energy will not change because energy is a function of frequency.

To answer this question, it's imperative to realize that we'll need to use the equation for the doppler effect. First, we'll need to calculate the frequency of the sound that reaches the wall. Then, we'll have to calculate the frequency of the reflected wave that reaches the bat.

The doppler effect equation is:

In the first case, we'll consider the frequency received by the wall. The bat is the source in this scenario, which is moving, while the wall is the stationary observer. Therefore, the  term in the above equation is 0. Moreover, since the bat is moving towards the wall, we should expect the frequency received by the wall to be larger than the original frequency. Hence, we will need to subtract the speed of the source in the denominator, since that will result in the expected increase in observed frequency.

Now that we have the frequency relfected from the wall, we can calculate the frequency that the bat will experience. In this scenario, the wall is now the source. But because it isn't moving, we can say that the  term in the doppler equation is 0. Likewise, the bat is now the observer in this case and is still moving at a speed of . Also, because the bat is moving towards the source, then conceptually we should expect the bat to observe a frequency that is greater than that reflected by the wall. To ensure this, we will need to add the  term in the numerator of the doppler equation.

The formula for the Doppler effect of the moving observer is:

Since the boy is approaching, the positive sign will be used. The velocity of sound is . Substitute the knowns into the formula.

This scenario deals with both a moving source and a moving observer.

Write the correct Doppler effect formula for this case.

Since the observer and the source are both approaching, the numerator will have a positive sign and the denominator will have a negative sign. The speed of sound is . Substitute all the knowns and find the frequency.

We are being told that two cars are moving towards one another, and one of the cars is emitting a sound at a certain frequency. The other car will, in turn, perceive this sound at a different frequency because both cars are moving relative to one another. Therefore, we can classify this problem as one involving the concept of the Doppler effect.

Since the two cars are moving towards one another, we can conclude that the observed frequency should be greater than the source frequency. In order to make that true, we'll need to add in the numerator above, and subtract in the denominator.

But we're not done yet. The question is asking for the perceived wavelength, not the perceived frequency. Hence, we'll need to convert frequency into wavelength using the following formula: