Question

A transverse wave is travelling on stretched string with velocity $u$. Tension in the string is $T$ and mass density of string is $\mu$. Find the velocity of cart $V$ such that waves seem stationary w.r.t cart.

• A. $\sqrt{\frac{T}{r}}$
• B. $2\sqrt{\frac{T}{r}}$
• C. $3\sqrt{\frac{T}{r}}$
• D. None of these

Answer 1

The correct option is A $\sqrt{\frac{T}{r}}$

As waves seem stationary w.r.t cart
$\therefore$ Velocity of wave w.r.t cart = 0
$V_{w/c}=V_{w/g}-V_{c/g}=0$
$\Rightarrow u-V=0$
$\Rightarrow u=V$
we know
$u=\sqrt{\frac{T}{\mu }}\therefore V=\sqrt{\frac{T}{\mu }}$