Grade by Grade
E. Waves and Sound · Waves and Sound

Waves and Sound: Unit Review

E1.1 E1.2 E2.1 E2.2 E2.3 E2.4 E2.5 E2.6 E2.7 E3.1 E3.2 E3.3 E3.4 E3.5 E3.6 A1.1 A1.5 A1.6 A1.8 A1.10 A1.11 A1.12 A1.13 A2.1 A2.2About 40 minutes
Learning goals
  • I can describe and calculate the properties of mechanical waves and sound.
  • I can explain interference, standing waves, beats, resonance and the Doppler effect.
  • I can solve problems about the speed of sound, air columns, decibels and echoes.
  • I can assess technologies that use or reduce waves and sound.

Words to know

universal wave equation
v = fλ.
superposition
When waves overlap, their displacements add.
standing wave
An interference pattern with fixed nodes and antinodes.
resonance
A large amplitude when a system is driven at its natural frequency.
Doppler effect
The change in observed frequency caused by a moving source.
decibel
The unit of sound intensity level; +10 dB = 10 times the intensity.

Let's review!

In this unit you described mechanical waves (transverse and longitudinal) with amplitude, wavelength, frequency and period, and linked them with the universal wave equation v = fλ. You saw how waves reflect and transmit at boundaries, how they superpose to make interference patterns, standing waves and beats, and how resonance picks out natural frequencies in strings, air columns, bridges and buildings. You studied sound: how it is produced and heard, how its speed depends on the medium and temperature, how loudness is measured in decibels, and how the Doppler effect changes the pitch of a moving source. Finally, you applied the physics to designs (instruments, concert halls, headphones, wave-energy buoys), to noise hazards, and to animals that hear sounds we cannot.

This review has a few questions from every lesson. Try each one, then press Show answer to check.

How to use this review

Do one or two sections at a time. Write every formula you use and include units in each answer. Use v = 343 m/s for air at 20 °C unless the question gives another value. Draw a quick sketch for boundary, interference, standing-wave and Doppler questions. For every question you get wrong, write down why (wrong formula? forgot to halve an echo time? sign error?) and go back to that lesson's worked examples. Finish with the 10-question quiz.

Describing wavesv = fλ and f = 1/Tenergy ∝ A²Sound in airv = 331 + 0.6T (m/s)echo: d = vt ÷ 2Strings and open pipesL = nλ/2fₙ = n v/(2L)Closed pipesL = (2n − 1)λ/4odd harmonics onlyBeats and Dopplerf_beat = |f₁ − f₂|f′ = f v/(v ∓ v_s)Interference and loudnesspath diff nλ: loud; (n + ½)λ: quiet+10 dB = ×10 intensity; I ∝ 1/r²
Your toolbox for this unit: the key equations, grouped by topic.
Mechanical wavesTransverseLongitudinalstrings, ropes, S-wavessound, P-waves, Slinky pushSuperpositioninterferencestanding wavesbeatsresonance
How the big ideas connect: mechanical waves are transverse or longitudinal, and superposition explains interference, standing waves, beats and (with natural frequencies) resonance.
Just for fun

Why did the physics student bring a Slinky to the unit test?

She heard the questions would come in waves.

Mechanical Waves: Pulses, Media and Energy Transfer

1

What does a wave transfer, and what does it not transfer?

2

Classify: a P-wave, a wave on a violin string, sound in water.

3

A pulse travels 7.2 m in 1.8 s. Find its speed.

Describing Periodic Waves: Amplitude, Wavelength, Frequency and Period

1

Crest to the next trough is 0.30 m. Find λ.

2

A wave has T = 0.0050 s. Find f.

3

Two points are 2.5λ apart. In phase or out of phase?

The Universal Wave Equation: v = fλ

1

f = 250 Hz, λ = 1.4 m. Find v.

2

A wave enters a slower medium. What happens to f, v and λ?

3

Find λ for a 2000 Hz tone in 343 m/s air.

Waves at Boundaries: Reflection and Transmission

1

A crest hits a fixed end. Describe the reflection.

2

A pulse goes from a heavy rope into a light rope. Describe the reflected and transmitted pulses.

3

An echo returns 1.5 s after a shout (v = 340 m/s). How far is the cliff?

Superposition and Interference

1

A +4 cm pulse meets a −6 cm pulse. Resultant at full overlap?

2

Two in-phase speakers, λ = 0.50 m. Path difference 1.25 m: loud or quiet?

3

What happens to two pulses after they pass through each other?

Standing Waves on Strings

1

Node-to-node distance is 0.35 m. Find λ.

2

A 0.80 m string has v = 240 m/s. Find f₁ and f₃.

3

How many loops does the 4th harmonic have?

Sound: A Longitudinal Pressure Wave

1

What is a rarefaction?

2

Which sound property sets pitch? Loudness?

3

Is 30 kHz audible to humans? What is it called?

The Speed of Sound in Solids, Liquids and Gases

1

Find v in air at −10 °C.

2

Rank steel, air and water by speed of sound.

3

Thunder arrives 4.5 s after lightning at 20 °C. Distance?

Loudness, Decibels and Noise Hazards

1

How many times more intense is 95 dB than 65 dB?

2

Distance from a source triples. New intensity?

3

At 88 dBA, how long is safe under Ontario's rule (85 dBA, 8 h, 3 dB exchange)?

4

Name one technology that reduces noise and how it works.

Resonance in Air Columns: Measuring the Speed of Sound

1

Closed tube, L₁ = 0.18 m, f = 480 Hz (ignore end correction). Find v.

2

L₁ = 0.155 m and L₂ = 0.495 m with a 512 Hz fork. Find v.

3

An open pipe is 0.50 m long at 20 °C. Find its first two resonant frequencies.

Resonance: Natural Frequency and Forced Vibration

1

State the condition for resonance.

2

A swing completes 10 swings in 24 s. How often should you push?

3

Give one way to protect a building from resonance.

Beats: Interference in Time

1

Find the beat frequency of 523 Hz and 528 Hz.

2

A string and a 440 Hz fork give 3 beats/s. Tightening the string makes 1 beat/s. Original frequency?

3

Why are beats an example of superposition?

The Doppler Effect and Sonic Booms

1

A 900 Hz source approaches at 25 m/s (v = 340 m/s). f′?

2

The same source moves away. f′?

3

A jet flies at 425 m/s where v = 340 m/s. Mach number?

Waves by Design: Instruments, Concert Halls, Headphones and Wave Energy

1

Why does a violin have a hollow wooden body?

2

How do noise-cancelling headphones work?

3

A reflection travels 30 m farther than direct sound (v = 343 m/s). Delay? Echo?

Echolocation, Infrasonic and Ultrasonic Hearing

1

A dolphin hears an echo after 0.060 s in sea water (1530 m/s). Distance?

2

Why do bats use high frequencies?

3

Why do whale and elephant calls travel far?

Check your understanding

Quiz

1.

Sound is a…

2.

A wave has f = 50 Hz and λ = 0.30 m. Its speed is…

3.

When a wave enters a new medium, which stays the same?

4.

A crest reflects from a fixed end as…

5.

The fundamental wavelength of a string fixed at both ends of length L is…

6.

The speed of sound in air at 25 °C is about…

7.

A tube closed at one end has a fundamental of 120 Hz. Its next resonant frequency is…

8.

Two tones of 440 Hz and 436 Hz produce…

9.

A siren moving toward you sounds…

10.

A 100 dB sound is how many times more intense than a 70 dB sound?

For parents and teachers

Use the review to find what to revisit:

  • Confusing transverse and longitudinal waves, or thinking the medium travels with the wave → Lesson 1 (Mechanical Waves).
  • Measuring amplitude or wavelength wrongly, or f/T mix-ups → Lesson 2 (Describing Periodic Waves).
  • Rearranging v = fλ, or not knowing what stays constant in a new medium → Lesson 3 (The Universal Wave Equation).
  • Wrong orientation of reflected pulses, or not halving echo times → Lesson 4 (Waves at Boundaries).
  • Sign errors when adding pulses, or path-difference mistakes → Lesson 5 (Superposition and Interference).
  • Node spacing (λ/2) or harmonic errors on strings → Lesson 6 (Standing Waves on Strings).
  • Pitch versus loudness, hearing range or parts of the ear → Lesson 7 (Sound).
  • Speed-of-sound and temperature calculations → Lesson 8 (The Speed of Sound).
  • Decibel arithmetic, inverse square law or noise-limit questions → Lesson 9 (Loudness, Decibels and Noise Hazards).
  • Closed versus open air columns, or the L₂ − L₁ method → Lesson 10 (Resonance in Air Columns).
  • Conditions for resonance, damping, bridges and buildings → Lesson 11 (Resonance).
  • Two possible answers in beat problems → Lesson 12 (Beats).
  • Doppler sign errors or Mach number → Lesson 13 (The Doppler Effect).
  • Technology assessments without physics → Lesson 14 (Waves by Design).
  • Echolocation, infrasound and ultrasound → Lesson 15 (Echolocation).

In Grade 12 Physics (SPH4U), these wave ideas return in the study of the wave nature of light, including interference and diffraction of light. Energy ideas from this unit connect to the Work, Energy and Power unit, and the Electricity and Magnetism unit explains how speakers and microphones turn electrical signals into sound and back.