Question

Fundamental frequency of a string stretched with a weight of 4kg is 256hz the weight required to produce its octave is

Answer 1

If the fundamental frequency of the spring is f

Then frequency of its octave is 2f.

f = K (T)1/2

2f = K(T')1/2

Hence T' = 4T

T' = 4*4 = 16 kg- wt

Answer 2

The weight required to produce its octave(T') = 16 kg

Explanation:

The fundamental frequency of the spring = $\nu$

∴ The frequency of its octave = $2\nu$

The string stretched with a weight (T) = 4 kg

To find, the weight required to produce its octave(T') = ?

We know that,

$\nu=K\sqrt{T}$            .....(1)

Also,

$2\nu=K\sqrt{T'}$       .......(2)

From equations (1) and (2), we get

$2K\sqrt{T}=K\sqrt{T'}$

⇒ $2\sqrt{T}=\sqrt{T'}$

Squaring both sides, we get

T' = 4T

⇒ T' = 4 × 4 kg = 16 kg

Hence, the weight required to produce its octave(T') = 16 kg