Question

Derive the equation for the frequency of vibration of a string ,which depends on
(a)length of the string (l)
(b) tension in the string (T)
(c)mass per unit length(μ)
Take the constant as 1/2.

Answer 1

Hey!

• Frequency = 1/time period

[ F ] = T^ ( - 1 )


• Tension = mass × acceleration

[ the quantity here used are only for dimension formula ]


[ t ] = MLT^(-2)


• Mass per unit length ( μ )


[ μ ] = ML^(-1)


[ Refer 1st attachment ]

Where , K is dimensionless quantity or said to be constant 1/2 !!



[ Swipe the image ]

$f = \frac{1}{2l} \sqrt{ \frac{t}{ \: μ } }$