The two traveling waves have the same angular frequency [itex] \omega [/itex], right? Now, what is the angular frequency of the resultant standing wave in terms of the angular frequency of the two standing waves? Is it twice the angular frequency of each traveling wave? I sit half of it? The same? One fourth?jcais said:Is the period of a comination wave the same as the period of two traveling waves that make up this combination standing wave?
I googled it, but found nothing as of yet concerning equal periods.
Thank you for your time.
No, this is the *period*. The period is in seconds. And it is the time it takes for a point to go from an extreme position (say y=+A) down and back to its initial position.jcais said:I am using an Excel document. It tells me to press F9 to make the waves move. The freq of the standing wave is easy to get. It is 3.15 seconds (the time it takes for an extreme to go back to an extreme).
that will be in Hz (Hz= 1/second) and that's the frequency.1/3.15 = period.
You can check it with the trig identities for adding trig functions. But yes,, the frequency of the combined wave is the same as the frequency of the individual waves (if each wave has the same frequency)I am supposed to press F9 to move the traveling waves from one extreme to another. I don't know what an extreme would be. But, I did it and guessed that the freq. is also 3.15. The way I am describing this is confusing, because there is not much detail in words.
So, I guess the 2 traveling waves have the same freq. as one combo standing wave making them both have the same period because T = 1/f, if I am correct.
Standing waves are a type of wave that appears to be stationary, with no net movement of energy. They are formed when two identical waves traveling in opposite directions interfere with each other. In contrast, traveling waves are waves that move through space, transferring energy from one point to another.
Some examples of standing waves include vibrations on a guitar string, sound waves in a closed pipe, and electromagnetic waves between two parallel plates. Standing waves can also be seen in natural phenomena, such as ocean waves bouncing off a cliff.
Nodes are points in a standing wave where the amplitude of the wave is always zero. These points represent areas of destructive interference, where the two waves cancel each other out. Antinodes, on the other hand, are points where the amplitude of the wave is always at its maximum. These points represent areas of constructive interference, where the two waves reinforce each other.
In standing waves, the wavelength is related to the frequency by the equation λ = 2L/n, where λ is the wavelength, L is the length of the medium, and n is the number of nodes (or antinodes) present in the standing wave. This means that as the frequency increases, the wavelength decreases and vice versa.
Standing waves have various real-world applications, including in musical instruments, where they produce distinct notes and harmonics. They are also used in microwave ovens to heat food, as the standing waves created by the microwave's magnetron cause water molecules in the food to vibrate and generate heat. Additionally, standing waves are used in earthquake detection, as they can be used to measure the properties of the Earth's interior.