Musical sound, noise pollution and the Doppler effect
Pitch depends on frequency, loudness on intensity, quality on overtones. The Doppler effect is a change in heard frequency when the source or listener moves.
Characteristics of musical sound
| Characteristic | Depends on | Example |
|---|---|---|
| Pitch (how shrill) | Frequency: higher frequency, higher pitch | A mosquito's buzz is high-pitched; a lion's roar is low-pitched, though much louder |
| Loudness | Intensity: energy carried per second per unit area | Turning up the volume of a radio raises the intensity and the loudness |
| Quality (timbre) | The overtones present with the main note, which decide the wave shape | The same note on a sitar and a flute sounds different; you know a friend's voice on the phone |
Intensity and the decibel
Intensity is the energy a wave carries per second across one square metre held at right angles to it. Our ears hear a huge range of intensities, so we use a logarithmic scale. The intensity level is β = 10 log(I/I₀), measured in decibels (dB). The reference I₀ = 10⁻¹² W m⁻² is the faintest sound a normal ear can hear, so it is 0 dB: the threshold of hearing. Each tenfold rise in intensity adds 10 dB. Near 120 dB sound starts to hurt: the threshold of feeling. The ear is most sensitive between about 2000 Hz and 3000 Hz. Loudness grows with intensity, but not in simple proportion. Pitch, loudness and quality are sensations, so they are subjective.
Common sound levels (typical values)
| Source | Level (dB) | Effect on a listener |
|---|---|---|
| Rustle of leaves | 10 | Quiet |
| Whisper | 20 | Quiet |
| Ordinary conversation | About 65 | Moderately loud |
| Busy street traffic | 70 to 80 | Loud |
| Motorbike, heavy vehicle | About 90 | Very loud |
| Jet plane taking off nearby | About 150 | Painful |
Noise pollution: effects and control
- Noise is unwanted sound loud enough to cause discomfort. Long exposure at 85 dB or more damages the inner ear and causes loss of hearing.
- Noise also raises the heartbeat, causes anxiety and sleeplessness, and can bring on severe headaches.
- Set up factories away from homes, and keep machines oiled and well maintained.
- Use better designs of engines and machines, and fit silencers.
- Limit loudspeakers and firecrackers, especially during festivals and processions.
- Plant trees along roads, use sound-absorbing materials, and wear ear muffs or plugs near loud machines.
The Doppler effect
Stand on a railway platform as a train passes, whistling. The pitch is higher as the engine comes towards you and lower as it goes away. This apparent change in frequency due to relative motion is the Doppler effect. The speed of sound is fixed by the air, not by the source. A source moving towards you crowds its waves together in front, so the wavelength is shorter and the frequency higher. Behind the source, the waves spread out. A listener moving towards a source meets more waves each second. Your NIOS lesson gives ν′ = ν(v − v₀)/(v − vₛ), with all speeds taken positive from source to listener. It works for light too: light from a receding star shifts towards red, the red shift, with Δλ/λ = vₛ/c.
Worked example: decibels and the red shift
(a) The intensity of sound from a loudspeaker is 10⁻⁵ W m⁻². Find its intensity level. (b) A spectral line from a star shows a red shift of 0.05 percent. Find the speed of the star and say whether it is coming closer or moving away. (I₀ = 10⁻¹² W m⁻², c = 3 × 10⁸ m s⁻¹)
- (a) β = 10 log(I/I₀) = 10 log(10⁻⁵ ÷ 10⁻¹²) = 10 log 10⁷.
- β = 10 × 7 = 70 dB.
- (b) Δλ/λ = 0.05/100 = 5 × 10⁻⁴.
- vₛ = c × Δλ/λ = 3 × 10⁸ m s⁻¹ × 5 × 10⁻⁴ = 1.5 × 10⁵ m s⁻¹.
- The wavelength has become longer (shifted to red), so the star is moving away.
(a) 70 dB; (b) 1.5 × 10⁵ m s⁻¹, moving away
An ambulance siren sounds higher as it races towards you and drops as it passes. Traffic police speed guns bounce microwaves off vehicles and use the Doppler shift to read their speed.
2 marks: “Distinguish between the pitch and the loudness of a sound.” Pitch: how shrill or flat a sound is; depends on frequency. Loudness: how strong it sounds; depends on intensity, which grows with the square of the amplitude.
2 marks: “What is the Doppler effect? Give two of its uses.” The apparent change in frequency due to relative motion of source and listener: higher when they approach, lower when they move apart. Uses: radar to find the speed of aircraft and vehicles; sonar to track submarines; red shift shows stars moving away.
1 marks: “The intensity of a sound increases 100 times. By how many decibels does its level rise?” 10 log 100 = 10 × 2 = 20 dB.
Pitch goes with Frequency, Loudness with Intensity, Quality with Overtones. Coming closer, the pitch goes higher.