First slide

Standing waves

Question

On a stretched string fixed at both ends, three possible wave lengths that can be generated are 90 cm, 60 cm and 45 cm. The length of the string may be

Easy

A

80 cm
B

120 cm
C

90 cm
D

45 cm

Solution

(3)
Length of the string,
$\begin{array}{l} l = n (\frac{λ}{2}) w h e r e n = 1, 2, 3, 4, ....... \\ \frac{λ}{2} d i s \tan c e b e t w e e n t w o a d j a c e n t n o d e s . \\ c l e a r l y w h e n l = 90 c m, n = 2 f o r λ = 90 c m, n = 3 f o r λ = 60 c m \\ a n d n = 4 f o r λ = 45 c m . \end{array}$
So minimum length of the string is 90 cm.

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