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💡 Length and beat
How long is one wave, and how many pass by each second? Those two ideas are wavelength and frequency.
What is wavelength?
- The distance between two consecutive crests (or two consecutive troughs).
- Represented by λ (Greek letter lambda).
- Its SI unit is the metre (m) .
What are frequency and time period?
- Frequency (ν) : the number of density oscillations at a point per second; SI unit hertz (Hz) .
- Time period (T) : the time for one complete oscillation; SI unit second (s) .
- They are inversely related: \(\nu = \dfrac{1}{T}\).
In this Activity, we will experiment as a class demonstration to identify the frequencies of musical notes using a mobile app.
- Open a frequency app such as Phyphox and use the ‘Audio Spectrum’ option (Hz).
- Sing the notes Sa, Re, Ga, Ma, Pa, Dha, Ni, Sa one after another.
- Record the approximate frequency of each note.
- Compare each note’s frequency as a ratio with Sa.
What we observe
Frequency is
lowest for Sa
and rises for higher notes — each note has a distinct frequency.
Example 10.1 — If there are 10 density
10 density oscillations in 2 s. Frequency \(=\dfrac{\text{oscillations}}{\text{time}}=\dfrac{10}{2}=5\ \text{Hz}\); time period \(=\dfrac{2}{10}=0.2\ \text{s}\).
⏸▶ Pause and Ponder
- 7. A thin band vibrates faster than a thick one, so it has a higher frequency and a shorter time period .
- 8. 20 Hz means 20 oscillations per second, so per minute \(=20\times 60=\mathbf{1200}\) oscillations.
- 9. Half of the wavelength from the graph (Fig. 10.19) is read directly as half the crest-to-crest distance.
NCERT Question 2 — For a sound wave propagating
For a sound wave propagating in a medium, increasing its frequency will increase its (i) wavelength (ii) speed (iii) number of compressions per second (iv) time period
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NCERT Question 3 — If 20 compressions pass a
If 20 compressions pass a point in 4 seconds, the frequency is (i) 80 Hz (ii) 5 Hz (iii) 10 Hz (iv) 0.2 Hz
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NCERT Question 5 — Graphs representing two sound waves
Graphs representing two sound waves are given in Fig. 10.30. If the scales on the X and Y axes of the two graphs are the same, which of the two sound waves has (i) greater wavelength, and (ii) smaller amplitude?
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NCERT Question 6 — The sound waves emitted by
The sound waves emitted by three sources A, B and C are represented in Fig. 10.31. If the frequency of A is maximum and C is minimum, identify the corresponding curves, and mark A, B and C on them.
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NCERT Question 13 — The variation of density of
The variation of density of medium for a sound wave propagating with a speed of 340 m s⁻¹ is shown in Fig. 10.32. Calculate the wavelength and frequency of the sound wave.
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NCERT Question 14 — The graphical representation of two
The graphical representation of two sound waves A and B propagating at the same speed of 345 m s⁻¹ is shown in Fig. 10.33. What is the wavelength of each of them? Also, calculate their frequencies.
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Important Definitions
- Wavelength — the distance between two consecutive compressions or two consecutive rarefactions.
- Frequency — the number of density oscillations at a point per second, measured in hertz.
- Time period — the time taken for one complete oscillation, measured in seconds.
