Question

a sonometer wire of length l vibrates in fundamental mode when excited by a tuning fork of frequency 416Hz.If the length is doubled keeping other things same, the string will vibrate with a frequency of
a. 416hz
b.208hz
c.832hz

Answer 1

b) vibrate with a frequency of 208 Hz

According to the relation of the fundamental frequency of a string
ν=12lFμ−−√
where
          l is the length of the string
           F is the tension
           μ is the linear mass density

We know that ν1 = 416 Hz, l1 = l and l2 = 2l.
v1∝1l1v1l1=v2l2(416)l=v2(2l)v2=208 Hz

Answer 2

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