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### Course: Physics archive>Unit 8

Lesson 5: Wave interference

# Derivation of beat frequency formula

In this video David derives the formula for beat frequency. Created by David SantoPietro.

## Want to join the conversation?

• If suppose there are two insrtuments one has 210 hz frequency and another havr unknown frequency but when we apply wax on the the that last intrument with the unknown frequency then also it is giving us the beat frequency as same as before without aplying wax can you please explain this phenomena
• Its possible to explain (but not to find the missing frequency)

Before explaining, are you happy about what beat frequencies are ? how they are caused??
• At why does he say it may not be an integer how would they construct by the same amount as the time before and not be an integar
• Maybe the wave with higher frequency, would meet the next wave at it's valley.. or somewhere in between. For the interference between the two waves to become constructive again, it doesn't only have to meet at the peaks.. maybe it can be somewhere else also.. Tell me if you get a better explanation..
• There are some equations of super position of waves which i dont understand .can any one please explain me that relates to sound ,wave amplitube after constructive and destructive interference.
• Two speakers that are facing the same direction can emit sound waves that are in phase with each other meaning the compressions and rarefactions line up with each other, an example of constructive interference. This increases the amplitude of the wave meaning the sound becomes louder. Destructive interference with sound is commonly seen in noise cancelling headphones which utilize an active noise control system. A microphone picks up the waveforms of the sound waves from the environment, and then the headphones emit sound waves that are the negative of (or out of phase with) the sound waves from the environment. Since the compressions and rarefactions don't line up, there is an occurrence of destructive interference decreasing amplitude and so ambient noise becomes quieter.
• so if I heard 8 wobbles when one of the note is 440 Hz so the frequency of other note is off by 8hz
• Right. The frequency of the other wave would be either 432 Hz or 448 Hz.
Because the wobbles = beats.
And the beats frequency is the difference between the frequencies of the waves.
(1 vote)
• What is the the pitch of the sound (resultant frequency) that we hear when two sound waves with the same amplitudes, same travelling speeds, same directions but different frequencies interfere? The mean of the two original frequecies or the biggest frequecy among the two original ones?
• You will hear beats. The difference in the frequencies will give the number of beats you will hear per second.
• What will be the beat frequency of sin(4t)+sin(7t) where 8 and 7 are w1 and w2. According to the formula it should be 3/(2pi) but when i graph it the frequency of the beat turns out to be 1/(2pi)
• Isn't the complete and more generalized formula (T_1 - T_2)*n_1 = T_2 *(n_1 - n_2)?