Sound Waves: Characteristics and Applications · Lesson 6 of 14
Wavelength, Frequency and Time Period
“Wavelength describes spatial repetition, frequency counts oscillations per second, and time period measures the duration of one oscillation.”
• Define wavelength frequency and time period. • State symbols and SI units. • Use the inverse relationship between frequency and time period. • Calculate frequency from oscillation count and time. • Interpret wavelength from a graph. • Relate musical notes to frequency.
A sound wave can repeat rapidly or slowly, and its repeating pattern can be closely spaced or widely spaced. Wavelength, frequency and time period allow these features to be measured precisely.
Characteristics of a Sound Wave
Wavelength, Frequency and Time Period
The distance between two consecutive crests or two consecutive troughs of a wave. It is represented by λ and measured in metres.
The number of density oscillations occurring at a fixed point per unit time. It is represented by ν and measured in hertz.
The SI unit of frequency. One hertz corresponds to one oscillation per second.
The time required for one complete density oscillation at a fixed point. It is represented by T and measured in seconds.
What Counts as One Oscillation?
At a fixed position, density can change from maximum to minimum and then back to maximum. That complete repeating change constitutes one oscillation. Equivalently, measuring from one crest passage to the next crest passage represents one full cycle.
Problem
Ten density oscillations occur in two seconds. Calculate frequency and time period.
- 1.Frequency is the number of oscillations divided by time.
- 2.ν = 10 ÷ 2 s = 5 Hz.
- 3.Time period is the time for one oscillation.
- 4.T = 2 s ÷ 10 = 0.2 s.
- 5.Check using T = 1/ν: 1/5 = 0.2 s.
Problem
A piston oscillates at 20 Hz. How many oscillations does it complete in one minute?
- 1.20 Hz means 20 oscillations every second.
- 2.One minute contains 60 seconds.
- 3.Number of oscillations = 20 × 60.
- 4.The piston completes 1200 oscillations.
Frequency and Musical Notes
Nearly single-frequency sounds can be produced using a tuning fork or careful whistling. The chapter proposes using a frequency-analysis app to compare musical notes such as Sa, Re, Ga, Ma, Pa, Dha, Ni and Sa. Different notes have different frequencies; in the described activity, the frequency rises as the sequence progresses.
Activity: Comparing Musical Frequencies
Use an audio-spectrum or tone-analysis tool to observe the frequency of different musical notes. Compare each measured frequency with the first Sa and look for patterns in the ratios.
Frequency answers 'how many cycles each second?' Time period answers 'how long for one cycle?' They carry the same information in reciprocal form.
Quiz
Which description best matches Wavelength?
Which description best matches Frequency?
Which term matches this description: The distance between two consecutive crests or two consecutive troughs of a wave.
Which term matches this description: The number of density oscillations occurring at a fixed point per unit time.
Which statement is a key takeaway from this lesson?
Practice Problems
- A sound has frequency 25 Hz. Find its time period.
- A vibration has time period 0.01 s. Find its frequency.
- Explain how to determine wavelength from a density-versus-distance graph.
- Why does a thin tightly stretched rubber band generally vibrate faster than a thicker one in the chapter's activity?
Key Takeaways
• Wavelength is the distance between two successive points in the same phase, such as two consecutive compressions. • Frequency is the number of complete oscillations produced each second and is measured in hertz. • Time period is the time required for one complete oscillation. • Frequency and time period are reciprocals: f = 1/T.