Question

Suppose you have a standing wave with three nodes and two anti-nodes (two vibrating segments). and the trequency is 60.0 Hz. You turn the knob on the controller so that the frequency now reads 55 Hz. How many anti-nodes do you expect to see? If the pattern is no longer a standing wave, this means 0 anti-nodes. I expect to see anti-nodes

Answer 1

When there is a standing wave with $n$ vibrating segments,

$L=n\frac{\lambda}{2}=\frac{n}{2}\frac{v}{f}$

$f=\frac{n}{2}\frac{v}{L}$

In the first case, $n=2$

$f_1=\frac{2}{2}\frac{v}{L}=\frac{v}{L}=60.0\,Hz$

Now the frequency is $f_2=55\,Hz$

$f_2=55\,Hz=\frac{n}{2}\frac{v}{L}$

$f_2=55\,Hz=\frac{n}{2}\frac{v}{L}=\frac{n}{2}(60.0)$

There is no integral number $n$ such that $55\,Hz=\frac{n}{2}(60.0)$

Hence there will be no standing waves on the string.

Answer is 0 antinodes