A string fixed ar both ends hus consecutive standing wave modes for which the distances between adjacent nodes are 18 cm and 16 cm respeco rively,
(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?

Explanation

Let I be the length of the string.
Then `18n=l.....(i)`
`16(n+1)=l.....(ii)`
From Eqs. (i) and (ii), wet get n = 8 and I = 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=2.88 m`
Speed of wave on the string
`v=sqrt((T)/(mu))=sqrt((10)/(4xx10^(-3)))=50m//s &`
`f=(v)/(lambda)=(50)/(2.88)=17.36 Hz`