# Does wave interference happen only to same frequency waves?

As the title says, from books and results from internet, I find that examples of wave interference always have the same frequency, only different in phase constant.

So, I'd like to know if wave interference happens only to same frequency waves

• Interference happens even when the frequencies are not the same, but then there can be no complete extinction. There will always be a beat frequency that is the difference of the two incoming frequencies. For many applications that is actually a good thing, because it is much easier and much more precise to detect such a beat frequency than a constant signal. One common application would be radar systems that estimate the doppler shift of an object by interference of the reflected signal with the original transmitter frequency. The beat frequency is then the doppler signal. – CuriousOne Dec 22 '14 at 16:14

No; wave interference takes place whenever two waves of any frequency, same, nearly the same or widely different interact. An air molecule next to your ear, for example, can only respond to the sum of all the different sound waves reaching it at any moment.

The results are simpler when the two waves are closely related, or some simple multiple of each other. One common effect caused by the interference closely related frequencies is the phenomenon of beats.

This video, MIT Physics Demo Tuning Forks Resonance & Beat Frequency 720 at about the $1:30$ mark, shows the result of adding two sound waves of almost the same frequency. The rider on the tine of one of the two tuning forks detunes it slightly. The two resulting waves can interferes constructively, then destructively, and then back again.

I've done this demonstration with a group of students around the apparatus. By asking the students to individually raise their hand when they heard the loudest sound, it becomes clear that the moment when the two waves arrive in step for any student depends on their position around the apparatus.

In the general case, with no assumptions about the frequency, shape, phase or amplitude of the two waves, the Superposition Principle applies.

Consider the first of the waves. What would the medium be doing at that instant, if this were the only wave acting? Say we're talking water waves, and the answer is that the water would be 20 cm above its normal position. Do the same for all the other waves present, keeping track of each answer, and noting in each case whether the water is above or below its undisturbed position. Finally, add up all the individual displacements. The result is the position of the water at that instant. Move forward a short period of time and repeat. The sequence of displacements versus time give nature of the resulting wave.

• Thank you, I would like to ask one more question if you don't mind. Is there any general equation for resultant wave of 2 wave that are different in Amplitude and frequency (or not). My textbook only have equation for ones have same amplitude and frequency. I might want the equation of ones different in amplitude if there exist one – aukxn Dec 22 '14 at 16:57
• @aukxn if you assume same amplitude and different frequency , then its basically just a trigonometric addition ($cos A + cos B$ if i remember correctly). about differing amplitudes i dont have any ideas now , will comment if i get any. – Gowtham Dec 22 '14 at 17:01
• @aukxn you may use phaser diagrams to get a resultant wave at a particular time – Pranav Rastogi Jan 15 '16 at 18:34

Usually examples in textbooks, the internet, and others will use two waves of the same frequency for experiments such as the Double Slit experiment, or else to show complete constructive or destructive interference. All EM waves will interfere with one another to varying degrees. Usually if we are considering frequencies in white light the intereference will be time-averaged, so ultimately have little effect on different wavelengths.

A useful mental comparison to make whenever interference is mentioned is to consider water waves on a flat surface that are being peturbed. If you generate a longer wavelength in one position and a shorter one a distance away, will they still combine to creative interference? It will not be such a simple combination as two waves of the same frequency, but you will still get moments of constructive and destructive interference.

The net result is a more complex wave, and you can get all kinds of shapes from combining waves. A nice site with a bit about the same effect but for sound waves can be found here: Hyperphysics Beat Frequencies