Two wires of the same material are stretched with the same force Their diameters are 1 2 mm and 1 - Physics - Waves

Question

Two wires of the same material are stretched with the same force
Their diameters are 1 2 mm and 1 6 mm, while their lengths are 90
cm and 60 cm respectively If the frequency of vibrations of first
is 256 hz,find that of the other

Kulshekhar Mehta · Accepted Answer

Two wires of the same material are stretched with the same force
Their diameters are 1 2 mm and 1 6 mm, while their lengths are 90
cm and 60 cm respectively If the frequency of vibrations of first
is 256 hz,find that of the other
The fundamental frequency of stretched string is given by
f=12LFμ
Here μ is mass per unit length means linear mass density

According to question,
f1f2=L2L1μ2μ2⇒256f2=6090πρr22πρr22=6090r2r1=6×1
69×1 2or, f2=2566×1 6×9×1 2=288 Hz
Hence required frequency is 288 Hz

Two wires of the same material are stretched with the same force.Their diameters are 1.2 mm and 1.6 mm, while their lengths are 90 cm and 60 cm respectively.If the frequency of vibrations of first is 256 hz,find that of the other.