Answer to Question #281913 in Mechanics | Relativity for Darkwidow

Question

secutive standing waves occur at frequencies 280 Hz and 315 Hz on a taut

g fixed at both ends. Determine the frequency of the 4th harmonic.

Answer 1

Explanations & Calculations

• The frequency of $\small n^{th}$ harmonic is given by,

$\qquad\qquad \begin{aligned} \small f_n&=\small \frac{nv}{2L} \end{aligned}$

• Then, for the consecutive frequencies: $\small n\,\&\,(n+1)$, since this arrangement allows for ll harmonics $\small n =1,2,3,...$

$\qquad\qquad \begin{aligned} \small 280&=\small \frac{nv}{2L}\\\\ \small 315&=\small \frac{(n+1)v}{2L}\\ &=\small \frac{nv}{2L}+\frac{v}{2L}\\ &=\small 280+\frac{v}{2L}\\ \small \frac{v}{2L}&=\small 35 \end{aligned}$

• Now for the fourth harmonic for which $\small n=4$, you can calculate the quantity: $\large\frac{4.v}{2L}$.