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Question

The given graph shows the displacement versus time relation for a disturbance traveling with a velocity of $ 1500 {\mathrm{ms}}^{-1}$. Calculate the wavelength of the disturbance.


Displacement (m) —> o D — E 3 G Time (in ps) —> A Time 5

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Solution

Step-1: Given data

Time Period(time taken to complete one wave) = 2μs=2×10-6s

The velocity of the wave = 1500ms-1

Step 2: Formula used

  1. Frequency of the wave (f) = 1timeperiod
  2. The wavelength and frequency of a wave are related as: v=; where v= velocity of wave; f=frequency of wave; and λ= wavelength of the wave.

Step-3: Calculate the wavelength (λ)

Frequency of the wave (f) = 1timeperiod= 12×10-6=1062=5×105Hz

The wavelength and frequency of a wave are related as: v=; where v= velocity of wave; f=frequency of wave; and λ= wavelength of the wave.

v=1500=5×105×λλ=300×10-5=3×10-3m

Hence, the wavelength of the wave is 3×10-3m.


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