Waves – Practice questions

Wave motion

1. (a) Distinguish between ‘transverse’ and ‘longitudinal’ waves.

(b) State ONE example each of transverse and longitudinal waves. (2 marks)

(c) In the wave equation, velocity ( v ), frequency ( f ) and wavelength ( λ ) are related. Write
the equation.

(iv) A wave motion has a frequency of 10 Hz and a wavelength of 250 m. Calculate

the speed of the wave. (2 marks)

2. A transverse progressive wave travels along a stretched string from left to right.

The shape of part of the string at a particular instant is shown in the figure below.
The frequency of the wave is 15 Hz.

Use the figure to determine, for this wave, the

(a) amplitude, in metres __________________________________ (1 mark)

(b) wavelength __________________________________ (1 mark)

(c) speed. __________________________________

 (b) The figure below shows a sinusoidal wave.

(i) Indicate on the figure above the amplitude of the wave. (1 mark)

Using the figure above, determine the wave’s

(ii) amplitude (in metres)

(iii) period (in seconds)

(iv) frequency (in hertz).

(6 marks)

(c) State ONE property of an electromagnetic wave. (1 mark)

1. (a) The diagram below represents a Displacement - Time graph of a waveform. This
represents a transverse wave.

(i) The wavelength of this wave is _____________ and the amplitude is

_____________.
 (ii) The number of cycles of this periodic wave per unit time is called the wave's
_________________, which has a value of _____________________.

(b) The figure below is a displacement-time graph representing a wave of wavelength 1.29
m.

For this wave determine the:

(i) amplitude, A, in metres

(ii) period, T

(iii) frequency, f

(iv) speed, v

2. (a) The figure below shows a Displacement – Time graph of a wavetrain.

(i) What is the frequency?

(ii) Sketch the curve of another wave of the same frequency and phase, but twice the
amplitude.

(b) (i) Draw a displacement-time graph to represent the movement of a floating buoy
which has an amplitude of 0.5 m as a water wave passes with a period of 3 s.
 (ii) Can the graph you drew in part (b) (i) be used to tell whether the wave is
transverse or longitudinal?

3. (a) A transverse seismic (earthquake) wave travels with a speed of 5 000 m s1 and causes
the ground to vibrate up and down. The graph in figure below shows the variation, with
time, of the displacement of the ground at a point, as the wave passes.

(i) Calculate the frequency of the wave.

(ii) Calculate the wavelength of the wave.

(iii) On the graph, draw two small crosses at the times at which the ground is moving
at the greatest rate. Explain your choice of points.

(iv) Write down a time at which the ground is stationary.

(v) On the axes shown in the figure below, draw a graph to represent a seismic wave
of half the amplitude and twice the frequency of the wave shown in figure
above. (4 marks)

(b) (i) State TWO differences between sound waves and electromagnetic waves.

(ii) Relate the terms “pitch” and “loudness” to the physical properties of a sound
wave.
 (iii) Describe an experiment to show that sound does not travel in a vacuum.

(c) The figure below shows how a sound wave travelling through a long, air-filled tube sets
up a periodic pattern of rarefraction and compression.

(i) Determine for this sound wave the

a) wavelength

b) frequency.

(ii) Is this frequency in the audible range. Justify your answer.

(speed of sound in air = 330 m/s)

Total 30 marks
2. (a) A transverse wave on the surface of a liquid has a wavelength of 1.8 cm. Explain what
is meant by a transverse wave and the wavelength of the wave. (2 marks)

(b) Figure 2 below is a displacement-time graph representing the wave described in part
(a) above.

(i) For this wave determine the

- amplitude ----------------
- frequency ----------------
- speed ----------------------

(6 marks)

(ii) Figures 3a and 3b below show the same wave striking a plane reflecting surface and incident on a
small gap in a plane, reflecting surface respectively. Complete the diagrams to show the wave (i) after
reflection and (ii) after passing through the
gap-
Figure 4 below shows the same wave approaching the gap which has been increased to five times its
original size. Complete Figure 4 to show the wave after it has passed through the gap.

(2 marks) Total 12 marks

3.
This question is concerned with the properties of three different kinds of waves.
(a) Speed, wavelength and frequency are properties of waves. Explain the meaning of each of these
terms when used in connection with a sound wave.
Wave speed_____________________________________________________________
Wavelength --------—----------------------------------------------------------------------------
Frequency --------------------------------------------------------------------------------------------
( 4 marks)

(b) (i) Figure 1 represents a number of adjacent wavefronts of a water wave in a ripple
tank.
Use Figure 1 to determine the wavelength of the water wave

(2 marks)

(ii) Figure 2 is the displacement vs time graph of a small leaf floating in the path of the water wave
in (i).

Determine the frequency of the wave by using the figure 2

(iii) Calculate the speed of the water wave.

( 3 marks)
(c) (i) Figure 3 shows a wave pulse at time t = 0, moving from left to right on a string.
(2 marks) Total 15 marks

(ii) The front of the pulse arrives at the position marked, X, at time t = 0.1 s. Sketch on the axes below,
a displacement vs. time graph for a small element of rope at X.

(d) The table below shows how the wavelength produced on a stretched string changes as
the wave speed is varied.
 Wave Speed, v /m s–1 Wavelength, λ /m

05 0.06

10 0.12

15 0.18

20 0.24

25 0.30

30 0.36

35 0.42

40 0.48

(i) Plot a graph Wave Speed, v versus Wavelength, λ. Draw the curve of best to
represent the data.

(ii) Hence, determine the frequency of the wave.

Sound

1.

(b) In 2010, Sound Navigation and Ranging (SONAR) was used to detect the presence of
submerged oil plumes in the Gulf of Mexico after a massive oil spill.

The figure below shows a ship using SONAR to locate an oil plume.

(i) Explain, with reference to the figure above, how SONAR was used to determine
the depth of an oil plume.

(ii) If echoes are received 0.3 seconds after being sent, calculate the depth of the oil
plume below the detector, given that

Distnce
Velocity = .
Time

[ Speed of sound in sea water = 1 450 m s –1 ]

2.  Ultrasound may be used to measure the depth of the sea. In the figure, a ship sends out pulses
of high-frequency sound (ultrasound) which are reflected from the sea bed and received at the
ship.

(a)        State three (2) other uses of ultrasound.     (2 marks)

(b)        The figure below is a trace of the pulses of ultrasound sent from the ship and the
reflected pulses. The speed of ultrasound in water is 1500 m/s.

An attempt was made to measure the wavelength of the ultrasound wave as shown
below. 

(i)         Determine the wavelength of the ultrasound.     (1 mark)

 
(ii)     Calculate the frequency of the wave.            (3 marks)

The pulse reflected from the sea bed and received at the ship every 7.5 ms.

 (iii)      Calculate the depth of the sea bed below the transmitter.     (3 marks) 
Electromagnetic waves

1. Electromagnetic waves consist of visible light and radiations higher or lower than the
wavelength of light.

(a) (i) Identify ONE type of radiation with wavelength:

a) longer than visible light _____________________________________

b) shorter than visible light. ____________________________________

(2 marks)

(ii) Complete the table below which relates to the sources and uses of
electromagnetic waves.

Name of Wave Source Use

X-ray To take X-ray pictures

Gamma Ray

Radio wave

(5 marks)

(b) (i) If gamma rays have a wavelength of 3.0 × 10 12 m, calculate the frequency of
this type of radiation. (3 marks)

(ii) Given that red light has a wavelength of 700 × 10 –9 m, calculate its frequency.
(4 marks)

[ Speed of all electromagnetic waves = 3.0 × 10 8 m s –1 ]

2. Electromagnetic waves of one wavelength are absorbed by a solar panel and waves of a longer
wavelength are emitted. If electromagnetic waves of wavelength

λ1 = 2 × 10−7 m are absorbed by a solar panel as shown in the figure above and waves of
wavelength λ2 = 6.5 × 10−5 m are emitted, calculate

(a)         the frequency in each case           (3 marks)

(b)         the decrease in frequency, Δf.            (1 mark)

 
(c) We assume that the useful energy transferred to the solar panel is a constant, k, times
the decrease in frequency of the e.m. waves. (E = k × Δf).

 State the corresponding energy transferred, E1 , in terms of k.    (1 mark)

(d)        With a change of conditions, the wavelength of the wave now absorbed by the panel
increased to λ3  =  6 × 10−7 m, but the emitted wavelength remains a λ2 = 6.5 × 10−5 m.
What fraction of E1, the original energy transferred, is now transferred to the solar
panel?                   (4 marks)

[Speed of light, c = 3.0 × 108 m s−1]

Reflection

(a)        Describe EACH of the following terms as it relates to the laws of reflection:

(i)        Normal        (1 mark)

(ii)        Angle of incidence

(iii)      Angle of reflection

(b)     In the description of the formation of an image produced in a plane mirror, a physics student
recalled FOUR (4) features.

(c)        State the laws of reflection.

(d)        Two mirrors, A and B, are inclined at an angle of 60° to each other.  Light strikes mirror A at
an angle of 30°, as shown in the figure below.

(i)        Determine the angle of incidence at mirror A.

 (ii)        Describe the path of the reflected ray after it leaves mirror B

1. (a) Describe EACH of the following terms as it relates to the laws of reflection:

(i) Normal

(ii) Angle of incidence

(iii) Angle of reflection

Describe what EACH of the terms means.

(3 marks)
(b) (i) With the aid of a labelled diagram, state the laws of reflection. (4 marks)

(ii) The glare of light from oncoming vehicles when driving on a rainy night can be
annoying. With the aid of a labelled diagram, show how this glare results.
(2 marks)
(c) In the description of the formation of an image produced in a plane mirror, a physics
student recalled THREE features.

State the THREE features of an image produced in a plane mirror. (3 marks)

(d) Using a relevant physics concept, explain why the word is painted in this manner at the
front of some emergency vehicles. (4 marks)
Refraction

1. (a) (i) State TWO examples of observations which provide evidence that light can be
refracted. (2 marks)

(ii) The figure below shows a ray of light travelling from air to water.

Complete the figure above by adding the normal at the point of incidence, the
refracted ray, and indicating the angles of incidence and refraction.
(3 marks)

(iii) As the light ray travels from air to water, determine if the speed of the light ray
will increase or decrease. Give a reason for your response. (2 marks)

2. An experiment was conducted to verify Snell’s law of refraction by measuring the angle of
incidence, i, and the angle of refraction, r, for a light ray entering a glass block. The data was
recorded as shown in the table below.

Angle of Angle of sin i

sin i sin r
Incidence, i Refraction, r sin r

30° 20° 0.50 1.47

50° 31° 0.52

60° 35° 0.87 0.57

(a) Complete the table above by inserting the missing values. (2 marks)

(b) Determine the angle of refraction if an incident angle of 70° was recorded for
this experiment. (Use the refractive index of glass as 1.52) (3 marks)
3. Testing of a new material to be used as an anti-reflective coating for eye glasses has yielded the
results shown in the table below.

Angle of incidence, î / ° 30.0 40.0 50.0 60.0 70.0

Angle of refraction, r / ° 23.5 30.5 38.0 43.7 48.5
sin î 0 0 0 0 0
sin r 0 0 0 0 0

(a) Complete the table above by calculating the values for sin î and sin r. (4 marks)

(b) Use the readings from the completed Table 1 to plot a graph of sin î against sin r on a
graph paper. (7 marks)

(c) Calculate the gradient of the graph. (4 marks)

(d) State the TWO laws of refraction. (4 marks)

(e) Calculate the angle of refraction if the angle of incidence is 90° for this new material.
(3 marks)

(f) The anti-reflective coating works best if its refractive index is the square root of the
refractive index of the lens in the eye glasses.

Determine the refractive index of the lens that gives the best result. (3 marks)

Total 25 marks

Total 15 marks
4. (a) State the laws of refraction. (6 marks)

(b) The figure below shows the clown fish, Nemo, looking at point B. It sees the
fisherman’s net appearing as if it were at A.

(i) Calculate angle c, given that angle ABD is 42o. (3 marks)

(ii) Given that angle c is the critical angle for the air–water boundary, calculate the
refractive index of the water. (3 marks)

(iii) Nemo swims away and his eye is now a horizontal distance of 5 metres from
point B. Looking at point B he no longer sees the net but now sees Bruce, the
shark.

If Bruce is at the same depth as Nemo, how far away is Bruce’s eye from
Nemo’s eye. Explain your result. (3 marks)
(c) A ray of red light emerges from a glass block as shown in the figure below.

If the block has a refractive index of 1.5, determine the value of the angle e.

(5 marks)

(d) A pencil is placed in a glass of water and appears to be bent as shown in the figure
below.

(i) Calculate the refractive index of the water which causes this apparent bending if
angle a = 32° and angle b = 45°. (3 marks)

(ii) If the pencil is now placed in ethanol with a refractive index of 1.36, calculate
the new angle b given that angle a in the ethanol remains at 32°. (4 marks)

(iii) Does the pencil bend more or less in ethanol than in water? Justify your answer.
(2 marks)
 Total 15 marks

(e) The figure below shows a ray of white light, AO, incident at 30° to the PS boundary of
the rectangular glass block, PQRS.

(i) Calculate the angle of refraction produced on the PS boundary.

(ii) Name the angle of refraction produced on the QR boundary.

(5 marks)

[ Refractive Index of glass = 1.5 ]

(f) A glass prism, as shown in the figure below, may be used to produce a spectrum.

(i) What is the name of the effect that is created? (1 mark)

(ii) On the figure above, trace the path of the white light into and out of the prism
indicating the red ray and the violet ray. (2 marks)