Question

A wire, fixed at both ends is seen to vibrate at a resonant frequency of $240Hz$ and also at$320Hz$

$\left(a\right)$What could be the maximum value of the fundamental frequency$?$

$\left(b\right)$ If transverse waves can travel on this string at a speed of $40m{s}^{-1}$, what is its length$?$

Answer 1

$\left(a\right)$Two frequencies are $v_1=240Hz$ and ${\nu }_2=320Hz$

So, Maximum fundamental frequency.

$$\begin{gathered} ={\nu }_2–{\nu }_1 \\ =320-240 \\ =80Hz \end{gathered}$$

Where $v_2$ is the second frequency

$v_1$ is the first frequency

$\left(b\right)$ Given$v=40m/s$

$$\begin{gathered} =>Lx80=0.5x40 \\ =>L=0.25m \end{gathered}$$

Where $L$ is the length

Therefore, the maximum frequency is $80Hz$and length is $0.25m$.