Physics - Wave on String Question with Solution | TestHub

Linear mass density $\mu =0.2$ kg/m and tension $T=80$ N.

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

The string vibrates in three segments, so $l=\frac{3\lambda }{2}$.

$\lambda =\frac{2l}{3}=\frac{2\times 0.6}{3}=0.4$ m.

Frequency $f=\frac{v}{\lambda }=\frac{20}{0.4}=50$ Hz.

Angular frequency $\omega =2\pi f=100\pi$ rad/s.

Amplitude $A=0.5$ cm $=0.005$ m.

Amplitude of transverse velocity $v_{max}=A\omega =0.005\times 100\pi =0.5\pi$ m/s.

$v_{max}=0.5\times 3.14=1.57$ m/s.

Answer: $1.57$ m/s