What are standing waves?
Standing waves are a common topic in physics and engineering, and they can be encountered in a wide variety of situations.
One such situation is in sound tubes and strings, where standing waves can cause unwanted resonance and interfere with the desired sound or vibration.
Sound tubes are cylindrical objects that are often used to amplify or direct sound waves.
When sound waves travel through a sound tube, they can reflect off the walls of the tube and interfere with each other, creating standing waves.
Strings, like those found on musical instruments such as guitars or violins, can also exhibit standing waves.
In this case, the standing waves are created by the tension and length of the string.
When a string is plucked or bowed, it vibrates at a certain frequency that is determined by its tension and length.
In this blog post, we’ll take a look at how to solve standing wave problems in these contexts.
1. Figure out what type of system we are working with
First things first, we need to know what type of system we are working with.
There are usually 3 types:
- Sound tube open at both ends
- Sound tube open at one end
- String
Once we know what system we are working with, we can pull the equations that we need off of our formula sheet.
2. Select a value of “n” to use in our equations
The value of n is going to tell us how many standing waves are being created in our system.
The largest wavelength and smallest frequency correspond to an n value of 1.
As the value of n increases, the wavelength with decrease and the frequency will increase.
3. Determine the wavelength of the standing wave
Now that we have the value of n, we can calculate the wavelength.
We just need to use the equation given for the system we are working with.
To see an example of how this is done, check out this youtube video.
4. Determine the speed of the wave
Now that we have the wavelength, we can determine the speed of the wave.
For standing waves in sound tubes, the speed of the wave will be the speed of sound.
For air, this is about 343 m/s.
For standing waves on a string, we can calculate the velocity using the tension of the string and the linear mass density of the string.
To see an example of how this is done, check out this youtube video.
5. Determine the frequency of the wave
Now that we have the wavelength and speed of the wave, we can calculate the frequency.
That’s the last step!
Check out the videos below to see specific problems solved.
Check out these YouTube videos to see solved examples
When I was in engineering school, I always started studying by watching YouTube videos (shoutout The Organic Chemistry Tutor).
Seeing other people solve problems helped me understand the thought process behind the steps to the solution.
Once I got the basics, I would start solving practice problems myself.
I am working on a Physics video series on YouTube where I go through theory and practice problems.
Check out these videos below!
Standing Waves Videos
Want extra practice problems with solutions? Check out my eBooks
Once you have watched a couple of YouTube videos, it’s time to practice for yourself!
Check out these physics eBooks with practice problems and full solutions.
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