CDS Physics · Formula sheet
Sound formulas
2 formulas, 4 reference tables and 12 common traps for CDS Physics Sound, grouped by subtopic.
Waves and the Speed of Sound
Learn this subtopic in the notesThe wave equation: speed, frequency and wavelength
Wave equation
- speed of the wave, in m/s
- frequency, in Hz
- wavelength, in m
- time period, in s
- time taken and distance covered
Longitudinal and transverse waves
| Wave | Type and medium |
|---|---|
| Sound in air | Longitudinal: compressions and rarefactions; needs a mediumQ CDS 2023 (I): sound and light in air are longitudinal and transverse respectively. |
| Light | Transverse electromagnetic wave; travels through a vacuum |
| Wave along a stretched string | Transverse; needs the string |
| Ripples on water | Transverse at the surface |
| Sound in a vacuum | Cannot travel: there is no mediumQ CDS 2018 (I): sound cannot pass through a hollow pipe kept in a vacuum. |
Speed of sound in different media
| Medium | Speed of sound (m/s, NCERT values) |
|---|---|
| Aluminium | 6420 |
| Steel | 5960Q CDS 2023 (II): of glass, stainless steel, water and oxygen, sound is fastest in steel. |
| Glass (flint) | 3980 |
| Sea water | 1531Q CDS 2024 (II): sea water is faster than distilled water, drinking water or methanol. |
| Distilled water | 1498 |
| Methanol | 1103 |
| Air at 25 °C | 346 |
| Oxygen | 316 |
Common traps
Sound and light are opposite kinds of wave
In air, sound is longitudinal and light is transverse. An option calling them both longitudinal, both transverse, or swapping the order is the usual trap.
A solid inside a vacuum still carries sound; a vacuum does not
Sound travels through any solid, liquid or gas, including a copper wire or a glass prism. What stops it is empty space: the inside of a pipe in a vacuum has no medium at all.
A crest and a trough together make one wave
Twenty crests with twenty troughs are twenty complete waves, not forty. Count pairs, then divide by the time to get the frequency.
Convert to metres and seconds first
A wavelength in centimetres or a distance in kilometres must be changed to metres before using , and kilohertz to hertz. Most wrong options come from a missed factor of 100 or 1000.
Denser is not the rule; stiffer is
Sound is fastest in solids because they are stiff (hard to compress), not simply because they are heavy. That is why steel beats glass and sea water beats fresh water. Among gases, the lighter hydrogen carries sound faster than oxygen.
A sonic boom needs a speed above the speed of sound, not light
A sonic boom comes from a source moving faster than sound. Nothing with mass can move faster than light, so that option is always wrong; moving exactly at or below the speed of sound gives no boom.
Pitch, Echo and Uses of Sound
Learn this subtopic in the notesEcho: finding a distance from the time
Distance from an echo
- distance to the reflecting surface
- speed of sound
- time from the sound to the echo (there and back)
Pitch, loudness and the human ear
| Characteristic of sound | Depends on |
|---|---|
| Pitch | FrequencyQ Asked twice: CDS 2020 (I) and 2022 (II). The answer is frequency, never amplitude or speed. |
| Loudness | Amplitude |
| Quality (timbre) | Waveform |
| One octave higher | Double the frequencyQ CDS 2019 (II): the note an octave above 500 Hz is 1000 Hz. |
| Sensitivity of the ear | Varies with frequency; best near 2 to 5 kHzQ CDS 2016 (II): the statement that the ear's sensitivity does not vary with frequency is the false one. |
Ultrasound, SONAR and transducers
| Device or term | What it does |
|---|---|
| Piezoelectric crystal | Produces ultrasound when an alternating voltage is appliedQ CDS 2017 (II): ultrasonic waves are produced using piezoelectric material. |
| SONAR | Measures distance under water from the echo of ultrasound |
| Ultrasound scanner | Forms images of organs inside the body |
| Microphone | Sound to electrical signal |
| Loudspeaker | Electrical signal to sound |
Common traps
Pitch is frequency; loudness is amplitude
A high-pitched sound is not a loud sound. Pitch goes with frequency, loudness with amplitude. Speed, wavelength and intensity are distractors in a pitch question.
An octave doubles the frequency; it does not add to it
One octave up means , two octaves up means . Adding half (500 to 750 Hz) or quadrupling for one octave are the usual wrong options.
Halve speed × time
The echo time covers the trip there and back. Speed × time gives twice the distance. For 330 m/s and 4 s the full product, 1320 m, is the wrong option set beside the right one, 660 m.
Watch the units in the options
660 m is 0.66 km, not 6.6 km or 0.066 km. Convert the answer before matching it.
Piezoelectric, not pyroelectric or ferromagnetic
Ultrasound generators use piezoelectric crystals, which vibrate under a voltage. Pyroelectric materials respond to heat, and ferromagnetic rods (magnetostriction) work only at much lower frequencies.
Microphone and speaker both deal in electrical signals
A microphone gives an electrical output, not a mechanical one, and a speaker takes an electrical input. The vibrating diaphragm inside is only a step on the way.