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Date May 2021 Marks available 2 Reference code 21M.2.SL.TZ1.6
Level Standard level Paper Paper 2 Time zone 1
Command term Outline Question number 6 Adapted from N/A

Question

On a guitar, the strings played vibrate between two fixed points. The frequency of vibration is modified by changing the string length using a finger. The different strings have different wave speeds. When a string is plucked, a standing wave forms between the bridge and the finger.

                                                       

The string is displaced 0.4 cm at point P to sound the guitar. Point P on the string vibrates with simple harmonic motion (shm) in its first harmonic with a frequency of 195 Hz. The sounding length of the string is 62 cm.

Outline how a standing wave is produced on the string.

[2]
a.

Show that the speed of the wave on the string is about 240 m s−1.

[2]
b.i.

Sketch a graph to show how the acceleration of point P varies with its displacement from the rest position.

                 

[1]
b.ii.

Markscheme

«travelling» wave moves along the length of the string and reflects «at fixed end» 

superposition/interference of incident and reflected waves

the superposition of the reflections is reinforced only for certain wavelengths  

a.

λ=2l=2×0.62=«1.24 m» 

v=fλ=195×1.24=242 «m s-1»

Answer must be to 3 or more sf or working shown for MP2.

b.i.

straight line through origin with negative gradient 

b.ii.

Examiners report

[N/A]
a.
[N/A]
b.i.
[N/A]
b.ii.

Syllabus sections

Core » Topic 4: Waves » 4.5 – Standing waves
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