How sound travels, what frequency and wavelength mean, and how echoes and sonar work.
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Sound is produced by vibrating bodies and needs a material medium; it cannot travel in a vacuum. In air it moves as a longitudinal wave: layers of compressions and rarefactions travel along the direction of the vibration. Terms: amplitude (largest displacement, related to loudness), frequency f (vibrations per second, in hertz, related to pitch), time period T = 1/f, wavelength λ (distance between two crests or compressions). The wave equation: v = f × λ.
A wave has frequency 500 Hz and wavelength 0.68 m. Find its speed.
v = 500 × 0.68 = 340 m/s.
Find the time period of a 500 Hz sound.
T = 1 ÷ 500 = 0.002 s.
Why can we not hear sound on the Moon?
There is no air, and sound needs a medium to travel.
The speed of sound is greatest in solids, less in liquids and least in gases: about 340 m/s in air at room temperature, about 1500 m/s in water and about 5000 m/s in steel. It rises with temperature and is unaffected by pressure. Humans hear 20 Hz to 20,000 Hz. Below 20 Hz is infrasound, above 20,000 Hz is ultrasound.
Find the wavelength at 20 Hz and at 20,000 Hz in air (340 m/s).
At 20 Hz: 340 ÷ 20 = 17 m. At 20,000 Hz: 340 ÷ 20000 = 0.017 m.
Arrange in order of speed: air, water, iron.
Air < water < iron.
Which has the higher pitch: 100 Hz or 1000 Hz?
1000 Hz; higher frequency means a higher pitch.
An echo is sound reflected from a distant hard surface and heard separately. Because the ear holds a sound for about 0.1 s, the reflecting surface must be at least v × 0.1 ÷ 2 away. Distance = v × t ÷ 2. Many echoes overlapping in a hall cause reverberation, reduced by curtains and acoustic tiles. Ultrasound is used in sonar, medical scanning and cleaning. Bats find insects with echoes.
An echo returns after 2 s. Find the distance to the cliff (v = 340 m/s).
d = 340 × 2 ÷ 2 = 340 m.
Find the minimum distance for a distinct echo.
d = 340 × 0.1 ÷ 2 = 17 m.
A sonar pulse returns from the sea bed in 0.4 s (v = 1500 m/s). Find the depth.
d = 1500 × 0.4 ÷ 2 = 300 m.
1. What is a longitudinal wave?
2. Define frequency and its unit.
3. Write the wave equation.
4. A source of 340 Hz makes sound of wavelength 1 m. Find the speed.
5. Why does sound not travel in a vacuum?
6. Give the audible range of humans.
7. What is the minimum distance for an echo?
8. An echo is heard after 1 s. Find the distance of the reflector (v = 340).
9. What does pitch depend on?
10. Name two uses of ultrasound.