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A string fixed at both ends has consecut...

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.
(a) What is the minimum possible length of the string?
(b) If the tension is 10 N and the linear mass density is 4 g/m, what is the fundamental frequency?

Text Solution

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The correct Answer is:
A, B, C, D
(a)
Let l be the length of the string. Then,
`18n =l` ………………(i)
16(n+1)=l…………..(ii)
From Eqs. (i) and (ii), we get
n=8
and l=144 cm
Therefore, the minimum possible length of the string can be 144 cm.
(b) For fundamental frequency, `l= lambda/2`

or `lambda = 2l =288 cm`
=288 m
Speed of wave on the string,
`v=sqrt (T/(mu))`
`=sqrt(10/(4xx (10^-3))) = 50 m/s`
`:. Fundamental frequency,`
`f=v/lambda = 50/2.88 `
=17.36 Hz
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