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

a.87.6 m/s

b.18.25 Hz

Step-by-step explanation:

the equation for the wave speed is expressed as

`v=\sqrt{(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{(8*2.40)/(0.0025) } \\v=87.6m/s\\`

b. the expression for the frequency is giving as

`Frequency,f=(v)/(2l) \\f=(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.