Question

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?

Answer 1

Tension  is 163.4 N

Explanation:

Mass 40 g (Spring) is attached to the tuning fork  

m = $40 \times 10^-^3 kgm^-^1$

The fork vibrates with f = 128 Hz

$\lambda$ = 0.5 m

v = $f\times \lambda$

= $128 \times 0.5$  

= $64\ ms^-^1$

But  

v = $\sqrt (\frac {T}{m}$

⇒ T = $v^2m$

= 163.84 N

Tension  is 163.4 N