Travelling Sine Wave MCQ - Practice Questions & Answers

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Sine wave travelling on string is considered one the most difficult concept.
14 Questions around this concept.

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Sine wave travelling on string

The sine wave or sinusoid is a mathematical function that describes a smooth repetitive oscillation.

$$
y(t)=A \sin (\omega t+\phi)
$$

Here $\omega$, is the angular frequency i.e,

$$
\omega=\frac{2 \pi}{T}=2 \pi f_{\text {It defines how many cycles of the oscillations are there. }}
$$

and $\phi=$ phase angle

General form:

a spatial variable x that represents the position on the dimension on which the wave propagates, and a characteristic parameter k called wave number which represents the proportionality between the angular frequency ω and the linear speed (speed of propagation ) ν. which is

$y(x, t)=A \sin (k x-\omega t+\phi)$ when the wave is moving towards the right
$y(x, t)=A \sin (k x+\omega t+\phi)$ when the wave is moving towards the left.
The wavenumber is related to the angular frequency by:

$$
k=\frac{\omega}{v}=\frac{2 \pi f}{v}=\frac{2 \pi}{\lambda}
$$

Also,

$$
\begin{aligned}
& \text { Particle velocity }=-(\text { wave velocity }) \times(\text { slope of } y \text { vs } \times \text { graph }) \\
& \Longrightarrow V_p=-v\left(\frac{\partial y}{\partial x}\right) \\
& \Longrightarrow \frac{\partial y}{\partial t}=-v\left(\frac{\partial y}{\partial x}\right)
\end{aligned}
$$