Question

A string of length 60 cm fixed at both end is vibrating in its 2nd overtone. If mass per unit length of string is 0.2 kg/m, tension in string is 80 N and maximum amplitude of standing wave is 0.5 cm, then maximum speed of any point of string is

• A. $50\pi cm/s$
• B. $40cm/s$
• C. $20\pi cm/s$
• D. $60\pi cm/s$

Answer 1

The correct option is A $50\pi cm/s$


Equation of standing wave is

$y=Asinkxcos\omega t$

Speed of any point of string is

$V_p=\frac{dy}{dt}=A\omega sinkxsin\omega t$ and $V_{p,max}=A\omega$

Wave velocity, $v=\sqrt{\frac{T}{\mu }}=\sqrt{\frac{80}{0.2}}=20m/s$

By $v=f\lambda \Rightarrow 20=f\times \frac{40}{100}\Rightarrow f=50Hz$

By $w=2\pi f=2\times \pi \times 50$

$\therefore V_{p,max}=\frac{0.5}{100}\times 2\pi \times 50=50\pi cm/s$