A sound has 13 crests and 15 troughs in 3 seconds. When the second crest is produced the first is 2cm away from the source? Calculate a) The wavelength, b) The frequency, c) The wave speed

 

Numerical: A sound has 13 crests and 15 troughs in 3 seconds. When the second crest is produced the first is 2cm away from the source? Calculate a) The wavelength, b) The frequency, c) The wave speed

Solution:

Given data:
Number of crests = 13
Number of troughs = 15
Time = 3 s

Step 1: Find number of complete waves

One complete wave = 1 crest + 1 trough

Total wave parts = 13 + 15 = 28
So, number of complete waves

$$n = \frac{28}{2} = 14 \text{ waves}$$

(a) Wavelength

When the second crest is produced, the first crest is 2 cm away from the source.
Distance between two successive crests = wavelength.

$$\lambda = 2 \text{ cm} = 0.02 \text{ m}$$

Wavelength = 0.02 m

(b) Frequency

$$f = \frac{\text{Number of waves}}{\text{Time}}$$ $$f = \frac{14}{3} \approx 4.67 \text{ Hz}$$

Frequency ≈ 4.67 Hz

(c) Wave speed

$$v = f \lambda$$
$$v = 4.67 \times 0.02 \approx 0.093 \text{ m/s}$$

Wave speed ≈ 0.093 m/s

Final Answers:

• Wavelength = 0.02 m

• Frequency ≈ 4.67 Hz

• Wave speed ≈ 0.093 m/s

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