Question

A wave travelling along a string is described by $y(x,t)=0.008\sin (85x-4t)$ in $\text{SI}$ units, where $x$ is in metres and $t$ is in seconds . Calculate the wavelength and frequency of the wave.

• A. $8.4\text{cm},1\text{Hz}$
• B. $14.8\text{cm},0.64\text{Hz}$
• C. $7.4\text{cm},1.28\text{Hz}$
• D. $7.4\text{cm},0.64\text{Hz}$

Answer 1

The correct option is D $7.4\text{cm},0.64\text{Hz}$

Given,
Equation of wave ,
$y(x,t)=0.008\sin (85x-4t)$
comparing the above equation with
$y(x,t)=A\sin (kx-\omega t),$ we get

Amplitude $\left(A\right)=0.008\text{m}$
Propagation constant $\left(k\right)=85{\text{m}}^{-1}$
Angular frequency $\left(\omega \right)=4\text{rad/sec}$

We know that, $\omega =2\pi f\Rightarrow f=\frac{\omega }{2\pi }$
From the data given in the question,
$f=\frac{4}{2\pi }=0.636\approx 0.64\text{Hz}$
Similarly ,
We know that ,
Angular wave number / Propagation constant $k=\frac{2\pi }{\lambda }$
$\Rightarrow \lambda =\frac{2\pi }{85}=0.0739\approx 7.4\text{cm}$

Thus, option (d) is the correct answer.