Wave behaviourIB Physics HL: Topic test

20 questions, 54 marks

IB Physics HL

Wave behaviour topic test

Total 54 marks

Name

Class

Date

1
A 0.25 kg mass hangs from a vertical spring of spring constant 40 N m⁻¹. It is pulled down 6.0 cm below its equilibrium position and released from rest, so that it oscillates with simple harmonic motion of amplitude 6.0 cm.
(a)
What is the period of oscillation of the mass?
[1 mark]
A0.50 s
B79.5 s
C0.079 s
D0.0063 s
(b)
What is the maximum speed of the mass during the oscillation?
[1 mark]
A0.06 m s⁻¹
B0.76 m s⁻¹
C9.6 m s⁻¹
D1.5 m s⁻¹
(c)
Calculate the speed of the mass when its displacement from equilibrium is 3.0 cm.
[2 marks]
Total for question 1: 4 marks
2
A loudspeaker emits a pure sound wave of frequency 850 Hz into still air, in which the speed of sound is 340 m s⁻¹.
(a)
What is the wavelength of the sound wave in air?
[1 mark]
A2.89 × 10⁵ m
B400 m
C0.40 m
D2.5 m
(b)
Which statement correctly distinguishes this sound wave from an electromagnetic wave of the same frequency?
[1 mark]
AThe sound wave is transverse while the electromagnetic wave is longitudinal
BThe sound wave travels faster than the electromagnetic wave through air
CBoth waves are transverse and can travel through a vacuum
DThe sound wave requires a material medium to travel through, while the electromagnetic wave can travel through a vacuum
(c)
Calculate the period of oscillation of the air particles due to this sound wave, and state whether this is the same as the period of oscillation of the loudspeaker cone producing the sound.
[2 marks]
Total for question 2: 4 marks
3
A ray of light travels inside a transparent block of refractive index 1.55, surrounded by air. It strikes a flat internal surface of the block at an angle of incidence of 42° to the normal.
(a)
Calculate the critical angle for the boundary between the block and the air, and determine whether total internal reflection occurs at this surface for a ray incident at 42°.
[3 marks]
(b)
After undergoing total internal reflection at the first surface, the ray strikes a second flat surface of the block at an angle of incidence of 25°, where it does emerge into the air. Calculate the angle of refraction of the emerging ray, and state what happens to its intensity compared with the intensity of the ray inside the glass just before this second surface.
[4 marks]
Total for question 3: 7 marks
4
A string fixed at both ends has a length of 0.90 m and a mass per unit length of 0.0040 kg m⁻¹. It is set vibrating in its second harmonic (first overtone) at a frequency of 240 Hz, forming a standing wave with one node between the two fixed ends. A small element of the string located at an antinode oscillates approximately in simple harmonic motion with amplitude 3.0 mm.
(a)
Determine the wavelength of the standing wave, the speed of the wave on the string, and the tension in the string.
[6 marks]
(b)
Treating the motion of the string element at the antinode as simple harmonic motion with the given frequency and amplitude, calculate its maximum speed and maximum acceleration. Explain how this SHM description of a single point relates to the standing wave pattern as a whole.
[6 marks]
Total for question 4: 12 marks
5
A police car's siren emits sound of frequency 660 Hz. The car moves directly towards a stationary pedestrian at a constant speed of 28 m s⁻¹. The speed of sound in the still air is 340 m s⁻¹.
(a)
What frequency does the pedestrian hear as the car approaches?
[1 mark]
A719 Hz
B610 Hz
C606 Hz
D714 Hz
(b)
How would the observed frequency change if the car were instead moving directly away from the pedestrian at the same speed?
[1 mark]
AIt would increase further above 660 Hz
BIt would decrease to below 660 Hz
CIt would remain equal to the approaching value of 719 Hz
DIt would drop to zero once the car is far enough away
(c)
Calculate the frequency heard by the pedestrian as the car moves directly away at 28 m s⁻¹.
[2 marks]
Total for question 5: 4 marks
6
A geologist uses a simple pendulum of length 1.20 m to estimate the local gravitational field strength. The pendulum is timed over 20 complete oscillations, which take a total of 44.4 s.
(a)
What is the period of oscillation of the pendulum?
[1 mark]
A44.4 s
B0.111 s
C2.22 s
D0.45 s
(b)
Why does the geologist time 20 oscillations rather than a single oscillation?
[1 mark]
ATo increase the amplitude of the swing
BTo keep the pendulum swinging for longer so that its length can be measured more accurately
CBecause it is not possible to time a single oscillation with a stopwatch
DTo reduce the percentage uncertainty in the period, since a fixed reaction-time error in starting and stopping the stopwatch is spread across many oscillations
(c)
Use these measurements to calculate a value for the local gravitational field strength g.
[2 marks]
Total for question 6: 4 marks
7
Monochromatic light of wavelength 589 nm from a sodium lamp passes through a single narrow slit of width 0.12 mm and forms a diffraction pattern on a screen 2.5 m from the slit.
(a)
Calculate the angle, from the centre of the pattern, to the first minimum of the single-slit diffraction pattern, and the distance from the centre of the pattern to this first minimum on the screen.
[3 marks]
(b)
A second, identical slit is now placed alongside the first, with the two slit centres separated by 0.60 mm, so that the pair produces a double-slit interference pattern modulated by the single-slit diffraction envelope found in (a). Calculate the fringe spacing of the interference pattern, and state how many bright interference fringes are seen within the central diffraction maximum (between the first diffraction minima on either side).
[4 marks]
Total for question 7: 7 marks
8
A distant galaxy emits a well-known hydrogen spectral line that, measured from a stationary laboratory source, has a wavelength of 656.3 nm. When the same line is observed in light received from this galaxy, it is measured at a wavelength of 661.0 nm.
(a)
Calculate the shift in wavelength of the spectral line, and use it to determine the speed of the galaxy relative to Earth, stating whether the galaxy is moving towards or away from the Earth.
[6 marks]
(b)
Calculate the frequency of the redshifted light (wavelength 661.0 nm) as measured on Earth. Explain, with reference to the wave equation v = fλ, why the speed of this light is still measured as 3.00 × 10⁸ m s⁻¹ on Earth, even though the source is moving and the wavelength has changed.
[6 marks]
Total for question 8: 12 marks

End of questions