A transverse harmonic wave on a string is described by y(x,t)=3.0… - Vidyadip

MCQ

A transverse harmonic wave on a string is described by $\text{y}(\text{x},\text{t})=3.0\sin(36\ \text{t}+0.018\text{x}+\pi/ 4)$ where x and y are in $cm$ and $t$ is in $s$. The positive direction of $x$ is from left to right.

A
The wave is travelling from right to left.
B
The speed of the wave is $20\ m/ s.$
C
Frequency of the wave is $5.7Hz.$
✓
All of the above

✓

Answer

Correct option: D.

All of the above

The standard from of a wave propagated from left to right i. e., in $+ve$ direction
$\text{y}=\text{a}\sin(\omega\text{t}-\text{k}\text{x}+\phi)$ and
$\text{y}=3.0\sin\Big(36\text{t}+0.018\text{x}+\frac{\pi}{4}\Big) ($given$)$
$a.$ As in given equation $x$ is in positive sigh so given wave travalling from right to left verifies option $(a)$
$b. \text{k}=0.018=\frac{2\pi}{\lambda}=0.018\Rightarrow\lambda=\frac{2\pi}{0.018}$
$\therefore\text{v}=\text{v}\lambda=\frac{18}{\pi}\times\frac{2\pi}{0.018}=2000\text{cm}/ \ \text{s}=20\text{m/ s}$
Verifies the option $(b)$
$c. \omega=36$ or $2\pi\text{n}=36$ or $\text{v}=\frac{36}{2\pi}=\frac{18}{3.14}=5.7\text{Hz}$
Verifies option $(c) n = 5.7Hz$

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