The time taken by a vibrating body to move from one extreme position to the other extreme position is 0.2 s. If the distance between adjacent crests is 4m, write the steps to determine the wave velocity in proper sequence.(a) Determine the frequency of the wave (f).(b) Note down the wavelength (λ).(c) Note down the time period (T).(d) Determine the velocity of the wave as v = fλ.
Question
The time taken by a vibrating body to move from one extreme position to the other extreme position is 0.2 s. If the distance between adjacent crests is 4m, write the steps to determine the wave velocity in proper sequence.(a) Determine the frequency of the wave (f).(b) Note down the wavelength (λ).(c) Note down the time period (T).(d) Determine the velocity of the wave as v = fλ.
Solution
Sure, here are the steps to determine the wave velocity:
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Determine the frequency of the wave (f): The frequency of the wave can be calculated by taking the reciprocal of the time period. Given that the time taken by a vibrating body to move from one extreme position to the other extreme position (which is half of the time period) is 0.2 seconds, the time period (T) is 0.2 x 2 = 0.4 seconds. Therefore, the frequency (f) is 1/T = 1/0.4 = 2.5 Hz.
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Note down the wavelength (λ): The distance between adjacent crests is given as 4m, which is the wavelength of the wave. So, λ = 4m.
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Note down the time period (T): As calculated in step 1, the time period is 0.4 seconds.
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Determine the velocity of the wave as v = fλ: Now that we have the frequency and the wavelength, we can calculate the velocity of the wave. Using the formula v = fλ, we get v = 2.5 Hz x 4m = 10 m/s.
So, the velocity of the wave is 10 m/s.
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