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Question
A particle on a stretched string supporting a travelling wave, takes 5⋅0 ms to move from its mean position to the extreme position. The distance between two consecutive particles, which are at their mean positions, is 2⋅0 cm. Find the frequency, the wavelength and the wave speed.
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Solution
Time taken to reach from the mean position to the extreme position,
\[\frac{T}{4}\] = 5 ms
Time period (T) of the wave:
\[T = 4 \times 5 ms\]
\[ = 20 \times {10}^{- 3} = 2 \times {10}^{- 2} s\]
Wavelength (λ) = \[2 \text{ times Distance between two mean positions}\] \[= 2 \times 2 cm = 4 cm\]
\[Frequency, f = \frac{1}{T}\]
\[ = \frac{1}{\left( 2 \times {10}^{- 2} \right)}\]
\[ = 50 Hz\]
\[ \text{Wave speed }, v = [\lambda f\]
\[ = 4 \times {10}^{- 2} \times 50\]
\[ = 200 \times {10}^{- 2} \]
\[ = 2 m/s\]
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