Wave behaviourIB Physics SL: Topic test

20 questions, 54 marks

IB Physics SL

Wave behaviour topic test

Total 54 marks

Name

Class

Date

1
A mass of 0.40 kg is attached to a horizontal spring of spring constant 250 N m⁻¹ on a frictionless surface. The mass is pulled 0.060 m from its equilibrium position and released from rest, undergoing simple harmonic motion.
(a)
What is the time period of the oscillation?
[1 mark]
A0.251 s
B157 s
C0.0400 s
D0.0100 s
(b)
What is the maximum speed of the mass during the oscillation?
[1 mark]
A0.239 m s⁻¹
B1.50 m s⁻¹
C37.5 m s⁻¹
D0.955 m s⁻¹
(c)
Determine the maximum acceleration of the mass during the oscillation.
[2 marks]
Total for question 1: 4 marks
2
A string of length 0.90 m is fixed at both ends. The speed of transverse waves on the string is 180 m s⁻¹.
(a)
What is the fundamental frequency of vibration of the string?
[1 mark]
A200 Hz
B50 Hz
C100 Hz
D300 Hz
(b)
What is the frequency of the third harmonic of the string?
[1 mark]
A200 Hz
B33.3 Hz
C400 Hz
D300 Hz
(c)
The string is made to vibrate at 500 Hz. Determine which harmonic this is, and state the total number of nodes present, including the two fixed ends.
[2 marks]
Total for question 2: 4 marks
3
A wave machine generates water waves that travel across the surface of a deep tank at a frequency of 4.0 Hz and a speed of 0.60 m s⁻¹. The waves then cross a boundary into a shallower region of the tank, where their speed decreases to 0.42 m s⁻¹, striking the boundary at 40° to the normal.
(a)
Determine the wavelength of the waves in the deep region of the tank, and state whether water waves of this kind are transverse or longitudinal, giving a reason.
[3 marks]
(b)
Determine the angle of refraction of the waves in the shallow region, and state whether the waves bend towards or away from the normal as they cross the boundary.
[4 marks]
Total for question 3: 7 marks
4
A string is stretched between two fixed points 1.2 m apart. The speed of transverse waves on the string is 60 m s⁻¹.
(a)
A single pulse is sent along the string from one end. Describe what happens to the pulse's shape, speed and orientation when it reflects from the fixed end, and explain, in terms of superposition, what happens while the incident and reflected pulses briefly overlap.
[6 marks]
(b)
Continuous waves are now sent along the string so that a stable standing wave pattern forms with exactly 3 antinodes. Determine the wavelength and frequency of this standing wave, and state the positions of all the nodes, measured from one fixed end.
[6 marks]
Total for question 4: 12 marks
5
In the laboratory, a particular hydrogen spectral line has a wavelength of 486.1 nm. The same line, observed in light from a distant galaxy, has a wavelength of 489.7 nm.
(a)
What does the observed wavelength being longer than the laboratory wavelength indicate about the galaxy's motion relative to Earth?
[1 mark]
AIt is moving towards Earth
BIt is moving away from Earth
CIt is stationary relative to Earth
DIt is moving perpendicular to the line of sight, so there is no effect on wavelength
(b)
What is the speed at which the galaxy is receding from Earth?
[1 mark]
A2.22 × 10⁶ m s⁻¹
B2.21 × 10⁶ m s⁻¹
C2.22 × 10³ m s⁻¹
D6.02 × 10⁸ m s⁻¹
(c)
A car's horn sounds at a constant frequency as the car is driven past a stationary observer at a constant speed, close to the roadside. Describe how the frequency heard by the observer changes as the car approaches, passes, and then moves away.
[2 marks]
Total for question 5: 4 marks
6
A simple pendulum has a length of 0.80 m. It is displaced so that its bob moves 0.050 m from the equilibrium position (a small angle, so the motion is simple harmonic) and released from rest.
(a)
What is the time period of the pendulum's oscillation?
[1 mark]
A0.512 s
B22.0 s
C0.286 s
D1.79 s
(b)
What is the maximum speed of the pendulum bob?
[1 mark]
A0.613 m s⁻¹
B0.0279 m s⁻¹
C0.175 m s⁻¹
D0.1115 m s⁻¹
(c)
Determine the maximum acceleration of the pendulum bob.
[2 marks]
Total for question 6: 4 marks
7
Water waves of wavelength 2.5 cm approach a harbour entrance 4.0 m wide, travelling at 1.2 m s⁻¹.
(a)
Determine the frequency of the water waves.
[3 marks]
(b)
Compare the amount of diffraction these waves show as they pass through the 4.0 m wide harbour entrance with the amount of diffraction that water waves of wavelength 8.0 m would show passing through a gap of the same width. Explain your reasoning.
[4 marks]
Total for question 7: 7 marks
8
A mass of 0.25 kg is attached to a horizontal spring of spring constant 60 N m⁻¹ on a surface with light damping (due to air resistance). The oscillator can be driven at varying frequencies by a vibration generator.
(a)
Determine the natural (resonant) frequency of the undamped oscillator. Describe how the amplitude of oscillation would vary as the driving frequency is increased slowly from zero, through resonance, and to well beyond it, and explain the effect that increasing the amount of damping would have on this resonance behaviour.
[6 marks]
(b)
Suppose instead the (undamped) oscillator is displaced 0.040 m from equilibrium and released from rest, undergoing simple harmonic motion at its natural frequency. Determine the total mechanical energy of the oscillation, and describe, in terms of kinetic and potential energy, how the energy of the system changes during one complete cycle.
[6 marks]
Total for question 8: 12 marks

End of questions