Standing Waves on a String: True/False Questions

In summary, the conversation discusses the formation of standing waves on a stretched string and the characteristics of these waves. The statements being discussed are whether the waves are transverse, if the highest resonant frequency is called the fundamental, if each end of the string must be a node, if the middle of the string can never be a node or an antinode, and if it is possible for half a wavelength to fill the length of the string. The correct answers are: True, False, True, False, True.
  • #1
BMWPower06
92
0

Homework Statement


A string of length L is stretched horizontally between two fixed points. When the string is plucked vertically, standing waves can be formed on the string. Which of the following statements are true about this situation?
True False The waves on the string are transverse waves
True False The highest resonant frequency is called the fundamental
True False Each end of the string must be a node
True False The middle of the string can never be a node or an antinode
True False It is possible for half a wavelength to fill the length of the string



The Attempt at a Solution



Answers are in bold, from reading through the chapter in my book i was able to come up with those answers, now the website says I am wrong but it doesn't tell me which one is wrong. Can any1 maybe help lead me in the right direction?

Thanks
 
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  • #2
The second one is false.

The fundamental note has the longest wavelength and therefore the lowest frequency.
 
  • #3
for your response!

1. True - The waves on the string are transverse waves.
2. True - The highest resonant frequency is called the fundamental.
3. False - Each end of the string must be a node.
4. False - The middle of the string can never be a node or an antinode.
5. True - It is possible for half a wavelength to fill the length of the string.

It seems like you have the majority of your answers correct! However, there is one statement that is false. Can you go back and double check your answer for statement #4? Remember that a node is a point where the amplitude of the wave is always zero, while an antinode is a point where the amplitude of the wave is always at a maximum. Based on this definition, can the middle of the string be a node or an antinode?
 

1. Is the amplitude of a standing wave on a string constant at all points?

No, the amplitude of a standing wave on a string varies at different points along the string. The nodes, where the string does not move, have an amplitude of zero while the antinodes, where the string moves the most, have the maximum amplitude.

2. Can standing waves on a string be created with only one end fixed?

Yes, standing waves on a string can be created with only one end fixed. This is known as a fixed-fixed boundary condition, where the string is anchored at both ends.

3. Is the frequency of a standing wave on a string determined by the tension and length of the string?

Yes, the frequency of a standing wave on a string is determined by the tension and length of the string. The frequency is directly proportional to the tension and inversely proportional to the length of the string.

4. Are there always an even number of nodes and antinodes in a standing wave on a string?

No, there can be an even or odd number of nodes and antinodes in a standing wave on a string. The number of nodes and antinodes depends on the mode of vibration of the standing wave.

5. Does the speed of the wave along the string change when a standing wave is formed?

Yes, the speed of the wave along the string changes when a standing wave is formed. The speed is reduced to half of the original speed, as the wave reflects back and forth between the fixed ends of the string.

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