Question

A wave is travelling on a string, the equation of which is given by,
$y=10\cos \left(2\pi \right(t-5x\left)\right)$
$x,y$ are in $\text{cm}$.

• A. The Time period of the wave is $1\sec$
• B. The wavelength of the wave is $10\text{cm}$
• C. The frequency of the wave is $1\text{Hz}$
• D. The Amplitude of the wave is $10\text{cm}$

Answer 1

Answer: (A), (C), (D)

The Amplitude of the wave is $10\text{cm}$

Comparing the given equation with standard equation of wave,

$y=A\cos (\omega t-kx)$

Amplitude, $A=10\text{cm}$

$\omega =2\pi$

$\Rightarrow T=\frac{2\pi }{\omega }=\frac{2\pi }{2\pi }$

$\Rightarrow T=1\sec$

Also, frequency, $f=\frac{1}{T}=1\text{Hz}$

From the given equation, $k=2\pi \times 5$

$\Rightarrow \lambda =\frac{2\pi }{k}=\frac{2\pi }{2\pi \times 5}=0.2\text{cm}$

Hence, options $\text{(A), (C)}$ and $\left(\text{D}\right)$ are correct.

Why this question? This question gives you understanding about all quantities involved in a wave equation. It helps you in revision of formula like $\lambda =2\pi /k,T=2\pi /\omega .$