A one metre long stretched string having a mass of 40 g is attached to a tuning fork. The fork vibrates at 128 Hz in a direction perpendicular to the string. What should be the tension in the string if it is to vibrate in four loops?

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Solution

A string of mass 40 g is attached to the tuning fork
$m = (40 \times 10^{- 3}) k g / m$
The fork vibrates with $f = 128 H z$
$λ = 0.5 m$
$v = f λ = 128 \times 0.5 = 64 m / s$
$v = \sqrt{T / m} \Rightarrow T = v^{2} m = 163.84 N \Rightarrow 164 N$ .

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A one metre long stretched string having a mass of 40 g is attached to a tuning fork. The fork vibrates at 128 Hz in a direction perpendicular to the string. What should be the tension in the string if it is to vibrate in four loops?

A string of mass 40 g is attached to the tuning forkm=(40×10−3)kg/mThe fork vibrates with f=128Hzλ=0.5mv=fλ=128×0.5=64m/sv=√T/m⇒T=v2m=163.84N⇒164N.

A string of mass 40 g is attached to the tuning fork
$m = (40 \times 10^{- 3}) k g / m$
The fork vibrates with $f = 128 H z$
$λ = 0.5 m$
$v = f λ = 128 \times 0.5 = 64 m / s$
$v = \sqrt{T / m} \Rightarrow T = v^{2} m = 163.84 N \Rightarrow 164 N$ .