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GCSE / IGCSE Physics – Waves

Wave properties, sound, EM spectrum, reflection and refraction.

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12 questions  ·  35 marks  ·  answers included  ·  GCSE / IGCSE Physics (Edexcel/AQA/Cambridge style)
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This worksheet covers:

  • Wave properties
  • Sound
  • The electromagnetic spectrum
  • Reflection and refraction

A calculator may be used; take the speed of sound in air as $340\,\text{m s}^{-1}$ and the speed of light in a vacuum as $3\times10^8\,\text{m s}^{-1}$ unless stated otherwise.

Questions

Section A – Wave Properties

1

(a) Define what is meant by the wavelength and the frequency of a wave.(b) State the wave equation linking wave speed $v$, frequency $f$ and wavelength $\lambda$.

Show answer
(a) Wavelength: the distance from one point on a wave to the identical point on the next wave (e.g. crest to crest). Frequency: the number of complete waves passing a point per second.(b) $v=f\lambda$.
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2

A sound wave in air has a frequency of $2.5\,\text{kHz}$. The speed of sound in air is $340\,\text{m s}^{-1}$. Calculate the wavelength of the sound wave.

Show answer
$\lambda=\dfrac{v}{f}=\dfrac{340}{2500}=0.136\,\text{m}$.
[2]
3

A water wave in a ripple tank has a frequency of $4.0\,\text{Hz}$ and a wavelength of $0.60\,\text{m}$. Calculate the speed of the wave.

Show answer
$v=f\lambda=4.0\times0.60=2.4\,\text{m s}^{-1}$.
[2]
4

Describe the difference between a transverse wave and a longitudinal wave, giving one example of each.

Show answer
In a transverse wave, the oscillations (vibrations) of the medium are perpendicular to the direction of energy transfer (e.g. light waves, water waves). In a longitudinal wave, the oscillations are parallel to the direction of energy transfer, producing compressions and rarefactions (e.g. sound waves).
[3]

Section B – Sound and the Electromagnetic Spectrum

5

Explain how a sound wave travels through air, and state why sound cannot travel through a vacuum.

Show answer
A vibrating source causes air particles to be pushed together (compressions) and pulled apart (rarefactions); these regions of higher and lower pressure travel outward, transferring energy without a net movement of particles. Sound cannot travel through a vacuum because there are no particles present to compress and vibrate.
[3]
6

List the seven regions of the electromagnetic spectrum in order of increasing frequency, and state one practical use each for microwaves and for gamma rays.

Show answer
Radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, gamma rays. Microwaves: satellite communication or cooking food. Gamma rays: sterilising medical equipment or treating cancer (radiotherapy).
[4]
7

A microwave has a frequency of $3.0\,\text{GHz}$. Calculate its wavelength in air, using $c=3\times10^8\,\text{m s}^{-1}$.

Show answer
$\lambda=\dfrac{c}{f}=\dfrac{3\times10^8}{3.0\times10^9}=0.10\,\text{m}$.
[2]
8

Explain the difference between ionising and non-ionising electromagnetic radiation, giving one example of each, and state one health risk associated with over-exposure to X-rays.

Show answer
Ionising radiation (e.g. X-rays, gamma rays, and high-frequency UV) has enough energy to remove electrons from atoms and can damage or mutate DNA in living cells. Non-ionising radiation (e.g. radio waves, microwaves, infrared) does not have enough energy to ionise atoms. Over-exposure to X-rays can cause cell mutation, increasing the risk of cancer.
[3]

Section C – Reflection and Refraction

Exam-style
9

State the law of reflection, and describe how the normal is used when drawing a ray diagram for reflection at a plane mirror.

Show answer
The law of reflection states that the angle of incidence equals the angle of reflection. The normal is a line drawn at right angles (90°) to the reflecting surface at the point where the ray strikes it; the angle of incidence and angle of reflection are both measured from this normal.
[2]
10

A ray of light travels from air into glass, striking the boundary at an angle of incidence of $40\degree$. The speed of light is $3.0\times10^8\,\text{m s}^{-1}$ in air and $2.0\times10^8\,\text{m s}^{-1}$ in the glass.(a) Calculate the refractive index of the glass relative to air.(b) Calculate the angle of refraction.

Show answer
(a) $n=\dfrac{v_{\text{air}}}{v_{\text{glass}}}=\dfrac{3.0\times10^8}{2.0\times10^8}=1.5$.(b) Using $n=\dfrac{\sin(\text{incidence})}{\sin(\text{refraction})}$: $\sin(\text{refraction})=\dfrac{\sin40\degree}{1.5}=0.4285$, so the angle of refraction is $25.4\degree$.
[4]
11

A glass block has a refractive index of $1.5$.(a) Calculate the critical angle for the glass-air boundary.(b) Explain what is meant by total internal reflection, and describe one practical application.

Show answer
(a) $\sin\theta_c=\dfrac{1}{n}=\dfrac{1}{1.5}$, so $\theta_c=41.8\degree$.(b) Total internal reflection occurs when light travelling in a denser medium hits a boundary with a less dense medium at an angle greater than the critical angle, so all the light is reflected back into the denser medium with no refraction. Application: optical fibres, used in telecommunications and medical endoscopes, rely on total internal reflection to carry light along the fibre with minimal loss.
[4]
12

A ray of light passes from air into a transparent block. The angle of incidence is $45\degree$ and the angle of refraction is $28\degree$.(a) Calculate the refractive index of the block.(b) State, with a reason, whether this material bends light more or less than the glass in the previous question.

Show answer
(a) $n=\dfrac{\sin45\degree}{\sin28\degree}=\dfrac{0.7071}{0.4695}=1.51$.(b) This is very close to (marginally greater than) the refractive index of the glass in the previous question ($n=1.5$), so the material bends light by almost exactly the same amount, very slightly more.
[3]

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