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 20m/ s.
C
Frequency of the wave is 5.7Hz.
D
The least distance between two successive crests in the wave is 2.5cm.

✓

Answer

The wave is travelling from right to left.
The speed of the wave is 20m/ s.
Frequency of the wave is 5.7Hz.

Explanation:

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)

As in given equation x is in positive sigh so given wave travalling from right to left verifies option (a)
$\text{k}=0.018=\frac{2\pi}{\lambda}=0.018\Rightarrow\lambda=\frac{2\pi}{0.018}$

$\therefore\text{v}=\text{v}\lambda=\frac{18}{\pi}\times\frac{2\pi}{0.018}=2000\text{cm}/ \ \text{s}=20\text{m/ s}$

Verifies the option (b)

$\omega=36$ 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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