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# A wave travelling on a string at a speed of 10 m s−1 causes each particle of the string to oscillate with a time period of 20 ms. (a) What is the wavelength of the wave? - Physics

Sum

A wave travelling on a string at a speed of 10 m s−1 causes each particle of the string to oscillate with a time period of 20 ms. (a) What is the wavelength of the wave? (b) If the displacement of a particle of 1⋅5 mm at a certain instant, what will be the displacement of a particle 10 cm away from it at the same instant?

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#### Solution

Given,
Wave speed (v) = 10 ms−1
Time period (T) = 20 ms
$= 20 \times {10}^{- 3} = 2 \times {10}^{- 2} s$
(a) Wavelength of the wave:

$\lambda = \nu t = 10 \times 2 \times {10}^{- 2}$

$= 0 . 02 m = 20 cm$
(b) Displacement of the particle at a certain instant:

$y = a\sin\left( \omega t - kx \right)$

$\Rightarrow 1 . 5 = a\sin\left( \omega t - kx \right)$
Phase difference of the particle at a distance x = 10 cm:
$\phi = \frac{2\pi x}{\lambda} = 2\pi \times \frac{10}{20} = \pi$

$The displacement is given by$

$y' = a\sin\left( \omega t - kx + \pi \right)$

$= a\sin\left( \omega t - kx \right) = 1 . 5 mm$

$\therefore Displacement = 1 . 5 \text{ mm }$

Is there an error in this question or solution?
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#### APPEARS IN

HC Verma Class 11, 12 Concepts of Physics 1
Chapter 15 Wave Motion and Waves on a String
Q 13 | Page 324
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