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Chapter 17: Q. 44 (page 485)

A 75 g bungee cord has an equilibrium length of 1.20 m. The

cord is stretched to a length of 1.80 m, then vibrated at 20 Hz. This

produces a standing wave with two antinodes. What is the spring

constant of the bungee cord?

Short Answer

Expert verified

The spring constant of the bungee cord is90N/m.

Step by step solution

01

Force and frequency 

Force and frequency are related to isometric force.

02

Solution of force and frequency 

Hooke's law represents force as F when it is present in spring.

The spring is constant which is k and elongated as x is F=kx

Here, the frequency comes from the stretched cord which is f=m2Lv=m2LT渭

It can be stated that L0is the length of the cord in an unstretched scenario. here L is stretched length and M is mass.f=m2Lk(L-L0)M/L=m2(L-L0)MLk

03

Explanation of the constant force

Ther force can be explained as

k=(m2L-L0ML)-2f2鈬�k=4f2ML(L-L0)m2

After subtracting the value contact will be

k=4.202路0.075路1.8(1.8-1.2)=90N/m

The stretch cords have created the sound waves but it does not create unstretched sounds.

Thus, linear density could be used for the stretched chords.

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