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, if any, of the statements below is/are true about this motion?
The middle of the string must always be a node.
The frequency of the second harmonic will be greater than the frequency of the first overtone.
When plucked near an end, usually multiple harmonic vibrational modes are excited.
When the string vibrates, pieces of the string move up and down.
There must be at least one anti-node. (T)
It is possible for two wavelengths to fill the length of the string.
The frequency of the 3rd harmonic will increse if the string tension is increased.
Each end of the string must be a node. (T)
All of the above statements are true.
The ones without (T) I believe are false, but apparently I am wrong. Any help please?
The middle of the string must always be a node.
The frequency of the second harmonic will be greater than the frequency of the first overtone.
When plucked near an end, usually multiple harmonic vibrational modes are excited.
When the string vibrates, pieces of the string move up and down.
There must be at least one anti-node. (T)
It is possible for two wavelengths to fill the length of the string.
The frequency of the 3rd harmonic will increse if the string tension is increased.
Each end of the string must be a node. (T)
All of the above statements are true.
The ones without (T) I believe are false, but apparently I am wrong. Any help please?
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The middle of the string must always be a node.
FALSE. The middle can vibrate.
The frequency of the second harmonic will be greater than the frequency of the first overtone.
FALSE. They are the same thing.
When plucked near an end, usually multiple harmonic vibrational modes are excited.
TRUE. The nearer the end you pluck, the more modes are possible (compare to plucking in the middle which tend to produce the fundamental because the antinode is in the middle)
When the string vibrates, pieces of the string move up and down.
TRUE. That's how a standing wave works.
There must be at least one anti-node.
TRUE. For the fundamental mode, there is 1 antinode. Higher modes have more.
It is possible for two wavelengths to fill the length of the string.
TRUE. This gives the 4th harmonic.
The frequency of the 3rd harmonic will increase if the string tension is increased.
TRUE. The fundamental frequency and all multiples of it (harmonics) increase if the string is tighter. That's why tightening a guitar string increases the pitch.
Each end of the string must be a node.
TRUE. The ends are fixed points so there can be no vibrations.
All of the above statements are true.
FALSE.
FALSE. The middle can vibrate.
The frequency of the second harmonic will be greater than the frequency of the first overtone.
FALSE. They are the same thing.
When plucked near an end, usually multiple harmonic vibrational modes are excited.
TRUE. The nearer the end you pluck, the more modes are possible (compare to plucking in the middle which tend to produce the fundamental because the antinode is in the middle)
When the string vibrates, pieces of the string move up and down.
TRUE. That's how a standing wave works.
There must be at least one anti-node.
TRUE. For the fundamental mode, there is 1 antinode. Higher modes have more.
It is possible for two wavelengths to fill the length of the string.
TRUE. This gives the 4th harmonic.
The frequency of the 3rd harmonic will increase if the string tension is increased.
TRUE. The fundamental frequency and all multiples of it (harmonics) increase if the string is tighter. That's why tightening a guitar string increases the pitch.
Each end of the string must be a node.
TRUE. The ends are fixed points so there can be no vibrations.
All of the above statements are true.
FALSE.