First slide

Standing waves

Question

A string fixed at both ends has consecutive standing wave modes for which the distances between adjacent nodes are 18 cm and 16 cm respectively. The minimum possible length of the string is

Easy

A

144 cm
B

152 cm
C

176 cm
D

200 cm

Solution

$L = \frac{{mλ}_{1}}{2} and L = \frac{(m + 1) λ_{2}}{2}$ , where m is number of harmonics
$\begin{array}{l} m \times 36 = (m + 1) \\ \Rightarrow m = 8 \Rightarrow L = 144 cm \end{array}$

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