Skip to content
Dabour HubLEARN · PRACTICE · EXPLORESign inStudent

Sound

Sound — American System Physics Revision Notes & Topical Questions

5 min read 6 parts Lesson 1 of 5 1 quiz

📚 American System Physics Hub / Topical Revision
🩺
100% Curriculum Specification Match Lesson Doctor Verified
The only platform with 100% curriculum specification match and verified interactive question banks.
0%read
Lesson summary

Sound: Properties, Detection and the Physics of Music — AMERICAN SYSTEM PHYSICS notes: Describe sound waves, pitch, loudness, decibels, echoes, resonance in strings and pipes, beats and the Doppler effect.Sound is a longitudinal wave of compressions and rarefactions that needs a medium.

  • sonic boom
  • Sound level
  • fundamental
  • Worked example 1
  • Worked example 2
  • Worked example 3

Section 1 of 6Sound waves, pitch and loudness

Sound is a longitudinal wave of compressions and rarefactions that needs a medium.

Speed in air is about 330-343 m/s and in water about 1500 m/s.
Pitch
Frequency determines pitch (how high or low a sound seems) and amplitude determines loudness (larger amplitude, louder).
Humans hear 20 Hz to 20 kHz; above this is ultrasound, used in medical imaging (safe because it does not ionise cells, unlike X-rays) and in sonar.
Bats use ultrasound up to about 100 kHz; short wavelengths let them detect small insects.
Echolocation uses reflected sound.
Sonic boom
A sonic boom is the loud shock wave heard when a source travels faster than sound, as wavefronts pile up into a cone.

The ear

  • the eardrum vibrates with pressure variations, the ossicles amplify the vibrations and the cochlea converts them to electrical nerve signals for the brain. Sound level is measured in decibels (dB) on a logarithmic scale: β = 10 log10(I/I0) with I0 = 10−12 W/m2.
  • 0 dB is the threshold of hearing, conversation about 60 dB, a rock concert about 110 dB and the pain threshold 120-130 dB.
  • Every +10 dB is ten times the intensity and +3 dB is about twice.

Noise-cancelling headphones use destructive interference of antiphase waves. In the Doppler effect an approaching source sounds higher in pitch.

Section 2 of 6Measuring sound and echoes

To measure frequency, connect a microphone to an oscilloscope near a loudspeaker driven by a signal generator.

Time-base
Adjust the time-base (time per horizontal division, for example 1 ms/div) and volts/div to display two or three waves.
Count the divisions for one wave and multiply by the time-base to get period T, then f = 1/T and compare with the generator.
Increasing the volume makes the trace taller with spacing unchanged; increasing frequency makes waves closer together with height unchanged.
More waves on the screen means higher frequency.

Sonar finds depth as follows

  • a transmitter on the hull emits a short ultrasound pulse downward at about 1500 m/s, it reflects from the seabed, a receiver detects the echo and a timer records total time t, and depth d = vt/2 is displayed.
  • For all echoes use distance = speed × time ÷ 2.

Section 3 of 6Resonance, harmonics and music

Every object has a natural frequency; resonance increases amplitude when driven at that frequency.

Fundamental
In an instrument the fundamental (first harmonic) is the lowest resonant frequency and determines pitch; harmonics are whole-number multiples.
A string or open pipe has fn = nv/(2L), n = 1, 2, 3 ...
A closed-pipe resonator is closed at one end: node at the closed end, antinode at the open end, resonant lengths L = λ/4, 3λ/4, 5λ/4 ... and only odd harmonics.
A longer string has a longer wavelength and lower fundamental, and tightening a string raises tension, wave speed and note.
Timbre (sound quality) depends on the mixture of harmonics.
Warmer air raises the speed of sound, so wind instruments rise in pitch.

Beats occur when two close frequencies interfere, alternately reinforcing and cancelling, so loudness rises and falls at |f1 − f2|; musicians tune until beats disappear. Consonant intervals have simple frequency ratios: octave 2:1, perfect fifth 3:2, fourth 4:3; dissonance results from close but unequal frequencies or complex ratios.

Section 4 of 6Worked examples

  1. Two tuning forks of 440 Hz and 444 Hz sound together. What is the beat frequency? [1]1 mark

  2. A sonar echo returns in 0.40 s; v = 1500 m/s. Find the depth. [2]2 marks

  3. A trace has period 2.5 ms. Find the frequency. [2]2 marks

  4. Increasing sound level by 20 dB multiplies intensity by how much? [1]1 mark

  5. What is the note one octave above 220 Hz? Why do a flute and violin playing the same note sound different? [3]3 marks

  6. Which harmonics are present in a closed pipe and why? [2]2 marks

Section 5 of 6Key terms

TermMeaning
PitchHow high or low a sound seems; determined by frequency.
LoudnessHow strong a sound seems, determined by amplitude.
Sound level (decibel)Logarithmic measure of intensity relative to the threshold of hearing; +10 dB is ten times the intensity.
Fundamental frequencyThe lowest resonant frequency of an instrument, the first harmonic.
Closed-pipe resonatorAn air column closed at one end with a node there and an antinode at the open end; only odd harmonics.
Time-baseThe oscilloscope setting giving the time represented by each horizontal division.
Sonic boomA shock wave heard when a source moves faster than the speed of sound.
BeatsPeriodic changes in loudness from interference of two close frequencies.

Section 6 of 6Exam technique

1
Saying a closed pipe has a node at the open end — the node is at the closed end.
2
Saying timbre depends on frequency — it depends on the mix of harmonics.
3
Calling beats echoes — they are periodic loudness changes from interference.
4
Forgetting to halve the time in echo calculations.
5
Saying a longer string gives a higher note — it gives a lower fundamental.

Last updated: