Waves, Sound & Optics — Chapter quiz · Physics & Environmental Science, Grade 12

Connect wave patterns, sound, electromagnetic radiation, interference, and refraction.

Problem 1

A wave has a frequency of 20 Hz and a wavelength of 5 m. Find its speed.
Answer and explanation

100 m/s

v = f × λ = 20 × 5 = 100 m/s.

Problem 2

A wave has a period of 0.05 s. Find its frequency.
Answer and explanation

20 Hz

f = 1 ÷ T = 1 ÷ 0.05 = 20 Hz.

Problem 3

In a longitudinal wave, the particles of the medium vibrate…
  1. in complete circles
  2. perpendicular to the direction of travel
  3. at right angles to the wave
  4. parallel to the direction of travel
Answer and explanation

parallel to the direction of travel

Longitudinal waves, like sound, have particles vibrating parallel to the direction the wave travels.

Problem 4

A sound wave in air has a frequency of 1715 Hz. Using the speed of sound as 343 m/s, find its wavelength.
Answer and explanation

0.2 m

λ = v ÷ f = 343 ÷ 1715 = 0.2 m.

Problem 5

The loudness of a sound is determined by its…
  1. frequency
  2. amplitude
  3. wavelength
  4. pitch
Answer and explanation

amplitude

Loudness depends on amplitude — a larger amplitude means a louder sound.

Problem 6

A radio wave has a frequency of 1 × 10⁸ Hz. Using the speed of light as 3 × 10⁸ m/s, find its wavelength.
Answer and explanation

3 m

λ = c ÷ f = (3 × 10⁸) ÷ (1 × 10⁸) = 3 m.

Problem 7

Light travels at 2.5 × 10⁸ m/s inside a transparent plastic. Using c = 3 × 10⁸ m/s, find its index of refraction.
Answer and explanation

1.2

n = c ÷ v = (3 × 10⁸) ÷ (2.5 × 10⁸) = 1.2.

Problem 8

Light passing from water into air (a lower-index medium) speeds up and bends…
  1. away from the normal
  2. toward the normal
  3. and stops
  4. and stays exactly parallel to the surface
Answer and explanation

away from the normal

Moving into a less dense, lower-index medium, light speeds up and bends away from the normal.

Problem 9

Two waves meet crest-on-crest, exactly in phase. This produces…
  1. constructive interference — the amplitudes add
  2. destructive interference — they cancel
  3. a doubling of the frequency
  4. a wave that stops moving
Answer and explanation

constructive interference — the amplitudes add

In-phase waves reinforce each other: constructive interference adds their amplitudes.

Problem 10

As a sound source moves toward you, the frequency you hear…
  1. stays exactly the same
  2. drops to zero
  3. increases, so the pitch rises
  4. decreases, so the pitch drops
Answer and explanation

increases, so the pitch rises

An approaching source bunches its wavefronts, raising the observed frequency and pitch — the Doppler effect.

Problem 11

Explain the following claim and supply a valid example or counterexample: A wave transfers energy without requiring bulk material travel with the pattern.
Answer and explanation

v=fλ=10 m/s andT=1/f=.20 s. A wave transfers energy without requiring bulk material travel with the pattern.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the calculation or mechanism that supports it.
  • Include units, conditions, or limits where relevant.

Problem 12

Independent chapter check: A wave has period0.020 s and wavelength0.80 m. Find frequency and speed. If frequency doubles in the same nondispersive medium, find the new wavelength.
Answer and explanation

f=50 Hz and v=40 m/s. At100 Hz with the same40 m/s speed, λ=0.40 m.

f=50 Hz and v=40 m/s.

At100 Hz with the same40 m/s speed, λ=0.40 m.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical or environmental mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

Problem 13

Explain the following claim and supply a valid example or counterexample: Sound requires a medium; pitch and loudness measure different aspects.
Answer and explanation

Round-trip 170 m; one-way distance 85 m. Sound requires a medium; pitch and loudness measure different aspects.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the calculation or mechanism that supports it.
  • Include units, conditions, or limits where relevant.

Problem 14

Independent chapter check: Two sound intensity levels differ by15 dB. Find their intensity ratio. A separate echo returns in0.30 s at340 m/s; find reflector distance.
Answer and explanation

The intensity ratio is10^1.5≈31.6. Echo distance=340×0.30/2=51 m; the two calculations use different models and quantities.

The intensity ratio is10^1.5≈31.6.

Echo distance=340×0.30/2=51 m; the two calculations use different models and quantities.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical or environmental mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

Problem 15

Explain the following claim and supply a valid example or counterexample: Electromagnetic waves share vacuum speed but have different frequencies and photon energies.
Answer and explanation

f=c/λ=1×10⁸ Hz. Use meters with SI c. Electromagnetic waves share vacuum speed but have different frequencies and photon energies.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the calculation or mechanism that supports it.
  • Include units, conditions, or limits where relevant.

Problem 16

Independent chapter check: A vacuum photon has wavelength400 nm. Find frequency and energy using c=3.00×10⁸ m/s and h=6.626×10⁻³⁴ J·s.
Answer and explanation

λ=4.00×10⁻⁷ m; f=7.50×10¹⁴ Hz and E=4.97×10⁻¹⁹ J per photon. This is not total beam energy without photon number.

λ=4.00×10⁻⁷ m; f=7.50×10¹⁴ Hz and E=4.97×10⁻¹⁹ J per photon.

This is not total beam energy without photon number.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical or environmental mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

Problem 17

Explain the following claim and supply a valid example or counterexample: Optically denser means higher refractive index, not necessarily greater mass density.
Answer and explanation

It slows in the simple model and bends toward the normal. Frequency stays continuous across a stationary boundary; wavelength changes. Optically denser means higher refractive index, not necessarily greater mass density.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the calculation or mechanism that supports it.
  • Include units, conditions, or limits where relevant.

Problem 18

Independent chapter check: A thin converging lens has f=12 cm and a real object at36 cm. Find image distance and magnification; describe the image.
Answer and explanation

1/di=1/12−1/36=1/18, so di=18 cm and m=−18/36=−0.50. It is real, inverted and half the object height in this paraxial model.

1/di=1/12−1/36=1/18, so di=18 cm and m=−18/36=−0.50.

It is real, inverted and half the object height in this paraxial model.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical or environmental mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

Problem 19

L=1 m,v=60 m/s fixed string. Find fundamental.
Hints

Write the relationship first; substitute with consistent units.

Answer and explanation

30 Hz

60/(2×1)=30.

Problem 20

What limits resonant amplitude in a real system?
Answer and explanation

Damping, energy losses, nonlinear behavior, and finite drive.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the calculation or mechanism that supports it.
  • Include units, conditions, or limits where relevant.

Problem 21

Independent chapter check: A1.5 m string fixed at both ends has wave speed30 m/s. Find its fundamental and third-harmonic frequencies and the third-harmonic wavelength.
Answer and explanation

f1=v/(2L)=10 Hz; f3=30 Hz. λ3=2L/3=1.0 m, with fixed-end nodes in this ideal string model.

f1=v/(2L)=10 Hz; f3=30 Hz. λ3=2L/3=1.0 m, with fixed-end nodes in this ideal string model.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical or environmental mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

Problem 22

Which direction of motion gives higher observed pitch in the basic case?
Answer and explanation

Approach compresses wavefronts and raises encounter frequency.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the calculation or mechanism that supports it.
  • Include units, conditions, or limits where relevant.

Problem 23

Distinguish pitch from loudness changes.
Answer and explanation

Pitch relates mainly to frequency; loudness relates to perceived intensity and depends on distance and other factors.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the calculation or mechanism that supports it.
  • Include units, conditions, or limits where relevant.

Problem 24

Independent chapter check: A600 Hz source recedes at30 m/s from a stationary observer in still air with sound speed330 m/s. Find received frequency and compare with the approach case at the same speed.
Answer and explanation

Receding:600×330/360=550 Hz. Approaching:600×330/300=660 Hz. The shifts are not symmetric about600 in this finite-speed source model.

Receding:600×330/360=550 Hz.

Approaching:600×330/300=660 Hz.

The shifts are not symmetric about600 in this finite-speed source model.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical or environmental mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

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