It is easy to observe the wave motion in a string but it doesn´t tell the whole story of wave properties. A string wave can't diffract or refract.
Sometimes simple explanations cause misunderstandings. Here a string wave is polarised by a narrow slit. Light, however, is polarised by a special Polaroid filter and not a slit.
Wave speed in a string
The velocity of a wave in a string is related to the tension and mass per unit length of the string:
\(v=\sqrt{T\over \mu}\)
Different guitar strings have different diameters and so different values of μ, mass per unit length. Therefore, the speed in each string will be different and they will vibrate with different frequencies.
Use quizzes to practise application of theory.
START QUIZ!
A wave in a string passes from a thin string into a thicker one.
Which diagram correctly represents the wave ?
A wave of wavelength 2m travels along a rope. The rope is attached to a second one which has the same diameter but 4 times the density.
What is the wavelength of the wave in the second rope?
v = √(T/m/L)
The mass per unit length is 4 times bigger.
The velocity is proportional to 1/√(m/L) so if m/L is x4 velocity is x 1/2
Wavelength is proportional to velocity
The velocity of a wave in a string is 2 ms-1. What will the velocity be if the tension in the string is changed from 20 N to 80 N
v = √(T/m/L)
The velocity is proportional to √T
T is x4 so velocity is x2
The axis below are velocity and Tension.
Which line is the correct shape for the velocity of a wave in a string vs the tension of the string?
A is 1/5x
B is y = x2
C is y = x
D is y = √x
A pulse moves towards the end of a string.
Here are diagram representing the string a short time later.
Which diagram represents the following situation
No end
Fixed end
Loose end
Connected to a thinner string
Connected to a thicker string
The diagram represents a pulse on a 1m long string fixed at both ends.
The following represent the string a short time later.
If the speed of the wave is 1ms-1, which diagram represents the string after the following times
1s
2s
3s
4s
The diagram represents a pulse in a 1m string with one fixed end and one loose end.
The following represent the string a short time later.
If the speed of the wave is 1ms-1, which diagram represents the string after the following times
1s
2s
3s
4s
Two pulses travel towards each other as shown.
The following represent the string a short time later.
If the speed of the wave is 1ms-1 which image represents the wave after:
0.5 s
1 s
1.5 s
2 s
5 s
Two pulses travel towards each other on a clamped string as shown.
The diagram below shows positions of the string some time later.
If the wave speed is 1 ms-1 which image represents the wave after:
1 s
5 s
9 s
13 s
Two pulses travel towards each other on a string that is clamped at one end and loose at the other.
The diagram below shows the string some time later
If the wave speed is 1 ms-1 which image represents the wave after:
1 s
5 s
9 s
13 s
18 s
Tow aves travelling towards each other cancel out as shown.
What form does the energy take when the waves cancel?
The string isn´t stretched or lifted but is moving even though it doesn´t look like it in the still image.
This diagram shows a wave approaching a narrow slit.
Which image shows the wave after passing through the slit?
Only the vertical component will pass.
The nodes in a standing wave are separated by:
The diagram represents a standing wave in a string.
Points A and B are
The diagram represents a standing wave in a string.
Points A and B are
The diagram represents a standing wave in a string.
Points A and B are
The diagram represents a standing wave in a string.
If the wavelength is 3m the distance between points A and B is:
The distance between antinodes is λ/2
The diagram represents a standing wave in a string
If the frequency of this wave is 12 Hz what is the frequency if the next harmonic?
This is the 3rd harmonic.
The frequency of the 1st harmonic = 4 Hz
The frequency of the 4th harmonic = 4 x 4 = 16Hz
The graph represents a frequency spectrum for a stretched string
The frequency of the 8th harmonic would be
1st harmonic = 50 Hz
8th Harmonic = 8 x 50 Hz
The graph represents the frequency spectrum for the string shown.
Át which point is the string being touched?
The 3rd harmonic is being played so there must be a node at 1/3 of the length
How much of Standing waves on a string have you understood?
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