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Difficulty: MediumProduction, Propagation, and Classification of Waves

A wave generator in a ripple tank creates periodic surface waves. An observer counts 45 complete wave crests passing a fixed marker in 15 seconds15\text{ seconds}. If the distance measured between the first crest and the seventh crest is 1.2 m1.2\text{ m}, what is the speed of propagation of the wave in m/s\text{m/s}?

Answer: 0.6 m/s

Answer

The speed of propagation of the wave is 0.6 m/s0.6\text{ m/s}.
The frequency is calculated as f=45 crests15 s=3 Hzf = \frac{45\text{ crests}}{15\text{ s}} = 3\text{ Hz}. The distance between the 1st and 7th crest spans 6 complete wavelengths (6λ=1.2 m6\lambda = 1.2\text{ m}), giving λ=0.2 m\lambda = 0.2\text{ m}. Applying the wave speed formula v=fλv = f\lambda yields v=3×0.2=0.6 m/sv = 3 \times 0.2 = 0.6\text{ m/s}.

Step-by-Step Solution

1
Calculate the frequency of the wave
Frequency f=3 Hzf = 3\text{ Hz}
Frequency is the rate at which complete wave cycles pass a fixed point, calculated as f=4515 s=3 Hzf = \frac{45}{15\text{ s}} = 3\text{ Hz}.
2
Calculate the wavelength from crest spacing
Wavelength λ=0.2 m\lambda = 0.2\text{ m}
The distance between nn successive crests contains (n−1)(n-1) full wavelength intervals. Thus, between the 1st and 7th crest there are 7−1=67 - 1 = 6 wavelengths, so 6λ=1.2 m  ⟹  λ=0.2 m6\lambda = 1.2\text{ m} \implies \lambda = 0.2\text{ m}.
3
Calculate wave speed using the fundamental wave equation
Speed v=0.6 m/sv = 0.6\text{ m/s}
Wave propagation speed is the product of frequency and wavelength: v=fλ=3 Hz×0.2 m=0.6 m/sv = f\lambda = 3\text{ Hz} \times 0.2\text{ m} = 0.6\text{ m/s}.

Key Concept

Wave speed calculation using frequency and wavelength derived from crest counting (v=fλv = f\lambda).
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Topics

Production, Propagation, and Classification of Waves

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