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Question 21M.2.HL.TZ1.8b.iii

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Date May 2021 Marks available [Maximum mark: 2] Reference code 21M.2.HL.TZ1.8b.iii
Level HL Paper 2 Time zone TZ1
Command term Calculate Question number b.iii Adapted from N/A
b.iii.
[Maximum mark: 2]
21M.2.HL.TZ1.8b.iii

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.

(b.iii)

Calculate, in m s−1, the maximum velocity of vibration of point P when it is vibrating with a frequency of 195 Hz.

[2]

Markscheme

max velocity occurs at x = 0 ✓

v=«(2π)(195)0.0042»=4.9 «m s−1» ✓

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