Question

A transverse wave having amplitude $A=\frac{4}{\pi }\text{m}$ and frequency $f=2\text{Hz}$ is travelling on a string of linear mass-density $\mu =1\text{kg/m}$. If the total kinetic energy associated with one wavelength of the wave is $16\text{J}$. Then the wavelength of the transverse wave is

• A. $0.5\text{m}$
• B. $0.25\text{m}$
• C. $0.75\text{m}$
• D. $0.15\text{m}$

Answer 1

The correct option is B $0.25\text{m}$

Total kinetic energy associated with one wavelength of the wave is given by,
$K_{\lambda }=\frac{1}{4}\mu A^2{\omega }^2\lambda$
$\because \omega =2\pi f=2\pi \times 2=4\pi \text{rad/s}$
$\text{and}A=\frac{4}{\pi }\text{m},\mu =1\text{kg/m}$
$\Rightarrow K_{\lambda }=\frac{1}{4}\times \lambda \times 1\times (4\pi {)}^2\times {\left(\frac{4}{\pi }\right)}^2$
$\Rightarrow 16=\frac{1}{4}\times \lambda \times 16\times 16$
$\Rightarrow \lambda =\frac{1}{4}\text{m}=0.25\text{m}$