Sound Waves: Characteristics and Applications · Lesson 8 of 14
Speed of Sound
“Wave speed connects wavelength and frequency and changes strongly with the medium, temperature and humidity.”
• Define speed of sound. • Derive and use the relation between speed wavelength and frequency. • Compare sound speeds in solids liquids and gases. • Explain temperature and humidity effects in air. • Solve wavelength frequency time period and distance problems. • Explain why frequency changes wavelength rather than speed in the same ordinary medium.
A compression created at one point does not appear everywhere instantly. It takes time for the density disturbance to move through the medium. The speed of sound tells us how quickly that disturbance propagates.
Speed of Sound
The distance travelled by a point on the wave, such as a crest or trough in its graphical representation, per unit time.
In one time period T, the wave advances by one wavelength λ. Therefore the speed equals wavelength divided by time period. Since ν = 1/T, the same relationship can be written using frequency.
Dependence on the Medium
The chapter states that sound generally travels fastest in solids, slower in liquids and slowest in gases. At the stated comparison conditions, approximate speeds are 5000 m s⁻¹ in steel, 1500 m s⁻¹ in water and 340 m s⁻¹ in air.
Temperature and Humidity
The speed of sound in air increases as temperature increases and also increases with humidity. The chapter gives about 331 m s⁻¹ in dry air at 0 °C and about 344 m s⁻¹ at 22 °C.
For ordinary media such as air, the speed is determined mainly by the medium and its conditions, not by the frequency of the source. If the frequency changes while the medium stays the same, wavelength changes so that v = λν remains satisfied.
Problem
Find the wavelengths corresponding to 20 Hz and 20 kHz in air when v = 344 m s⁻¹.
- 1.Use λ = v/ν.
- 2.For 20 Hz: λ = 344/20 = 17.2 m.
- 3.For 20 kHz, convert first: 20 kHz = 20,000 Hz.
- 4.λ = 344/20,000 = 0.0172 m.
- 5.Convert 0.0172 m to centimetres: 1.72 cm.
- 6.The two wavelengths are 17.2 m and 1.72 cm.
Problem
Lightning is seen and thunder is heard 5 s later. Estimate the distance if sound speed is 340 m s⁻¹ and light travel time is neglected.
- 1.Use distance = speed × time.
- 2.Distance = 340 m s⁻¹ × 5 s.
- 3.Distance = 1700 m.
- 4.Convert to kilometres: 1700 m = 1.7 km.
- 5.The lightning strike is approximately 1.7 km away.
Problem
A graph for sound in steel shows consecutive corresponding crests 50 m apart. If v = 5000 m s⁻¹, find frequency and time period.
- 1.The crest-to-crest distance is one wavelength, so λ = 50 m.
- 2.Use ν = v/λ = 5000/50.
- 3.ν = 100 Hz.
- 4.Use T = 1/ν = 1/100.
- 5.T = 0.01 s.
Problem
Two people are 340 m apart. Use 340 m s⁻¹ for air and 5000 m s⁻¹ for steel. Find the arrival-time difference.
- 1.Time through air = 340/340 = 1.0 s.
- 2.Time through steel = 340/5000 = 0.068 s.
- 3.Difference = 1.0 − 0.068 = 0.932 s approximately.
- 4.This is greater than 0.1 s, so the two arrivals could be distinguished separately under the criterion stated in the chapter.
At fixed wave speed, frequency and wavelength vary inversely: increasing frequency means reducing wavelength. Do not assume that a higher-pitched source automatically makes sound travel faster through the same ordinary medium.
Quiz
Which description best matches Speed of Sound?
Which term matches this description: The distance travelled by a point on the wave, such as a crest or trough in its graphical representation, per unit time.
Which statement is a key takeaway from this lesson?
Which additional statement is also a key takeaway from this lesson?
Which further statement is also a key takeaway from this lesson?
Practice Problems
- Find wavelength for a 100 Hz sound travelling at 340 m s⁻¹.
- Find frequency for wavelength 3.44 m at speed 344 m s⁻¹.
- Calculate the ratio of sound speed in water to sound speed in air using 1500 m s⁻¹ and 340 m s⁻¹.
- Explain why thunder reaches you after the lightning flash.
Key Takeaways
• The speed of a wave is related to its frequency and wavelength by v = fλ. • Sound travels at different speeds in different media. • It generally travels faster in solids than in liquids and faster in liquids than in gases. • The speed of sound in air also changes with conditions such as temperature and humidity.