Question 21M.2.HL.TZ1.8
| Date | May 2021 | Marks available | [Maximum mark: 12] | Reference code | 21M.2.HL.TZ1.8 |
| Level | HL | Paper | 2 | Time zone | TZ1 |
| Command term | Calculate, Estimate, Outline, Show that, Sketch, State | Question number | 8 | Adapted from | N/A |
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]
«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 ✓
Show that the speed of the wave on the string is about 240 m s−1.
[2]
✓
✓
Answer must be to 3 or more sf or working shown for MP2.
Sketch a graph to show how the acceleration of point P varies with its displacement from the rest position.
[1]
straight line through origin with negative gradient ✓
Calculate, in m s−1, the maximum velocity of vibration of point P when it is vibrating with a frequency of 195 Hz.
[2]
max velocity occurs at x = 0 ✓
✓
Calculate, in terms of g, the maximum acceleration of P.
[2]
✓
✓
Estimate the displacement needed to double the energy of the string.
[2]
use of ✓
✓
The string is made to vibrate in its third harmonic. State the distance between consecutive nodes.
[1]
✓