Question

A rope supports a standing wave with a total of 4 nodes. It fixed at the both ends.Calculate the frequency of the wave if the length of rope is 6 m and wave can travel at 40 m/s down the rope.

• A. 6.7 Hz
• B. 10.0 Hz
• C. 13.3 Hz
• D. 20.0 Hz
• E. 26.7 Hz

Answer 1

Answer: (B)

10.0 Hz

As rope is fixed at both ends so at both fixed ends there will be two nodes and rest of two will be in between of them. It is given that rope has four nodes, therefore length of rope $L=\frac{3\lambda }{2}$

but given that $L=6m$

so, $6=\frac{3\lambda }{2}$

or $\lambda =4m$

now frequency $f=\frac{v}{\lambda }$ (given $v=40m/s$)

$f=\frac{40}{4}=10Hz$