Question

A 240 cm length of string has a mass of 2.5 g. It is stretched with a tension of 8.0 N between fixed supports. (a) What is the wave speed for this string? (b) What is the lowest resonant frequency of this string?

Answer 1

Answer:

a.87.6 m/s

b.18.25 Hz

Explanation:

the equation for the wave speed is expressed as

$v=\sqrt{\frac{Tl}{m}}$

where v is the speed,

           T is the tension in Newton

           l is the length

and      m is the mass

Now since

$T=8.0N\\m=2.5g=0.0025kg\\l= 240cm=2.40cm$

by substituting values into the equation, we have

$v=\sqrt{\frac{8*2.40}{0.0025} } \\v=87.6m/s$

b. the expression for the frequency is giving as

$Frequency,f=\frac{v}{2l} \\f=\frac{87.6}{2*2.40} \\f=18.25Hz$.

Note we 2L as the wavelength because we solving for the fundamental frequency as stated in the question.