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Waves — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysicsWaves5 Marks
Question
A transverse harmonic wave on a string is described by
$\text{y}(\text{x, t})=3.0\sin\big(36\text{t}+0.018\text{x}+\frac{\pi}{4}\big)$
where x and y are in cm and t in s. The positive direction of x is from left to right.
Is this a travelling wave or a stationary wave?
If it is travelling, what are the speed and direction of its propagation?
✓

Answer

Yes; Speed = 20 m/s, Direction = Right to left
Explanation:
Given,
$\text{y}(\text{x, t})=3\sin\big(36\text{t}+0.018\text{x}+\frac{\pi}{4}\big)$
We know, the equation of a progressive wave travelling from right to left is:
$\text{y}(\text{x, t})=\text{a}\sin(\omega\text{t}+\text{kx}+\phi)\ \dots(2)$
Comparing equation (1) to equation (2), we see that it represents a wave travelling from right to left and also we get:
$\text{a}=3\text{cm},\omega=36\text{rad/s},\text{k}=0.081\text{cm and }\phi=\frac{\pi}{4}$
Therefore the speed of propagation, $\text{v}=\frac{\omega}{\text{k}}=\frac{36}{0.018}=20\text{m/s}$

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