1. If you want to double the wave speed, by what factor should you change the te

Question

1. If you want to double the wave speed, by what factor should you change the tension? Why? (Assume that the linear mass density does not change.)

2. If the wave speed is doubled, what will happen to the fundamental frequency f1? Why?

3. If the initial tension in the string is (2.00  ± 0.01) N, calculate the tension (and its uncertainty) that would double the wave speed.

Relevant equations:

The frequencies of the standing waves are called resonance frequencies fn

n = 1, 2, 3, 4… is called the harmonic number (or the number of antinodes)
v is the speed of the wave on the string
L is the length of the string between the fixed ends

µ = mstring/LTotal

Explanation / Answer

1)

speed v=sqrt(T/u)

here,

T is tension,

u is linear mass density

speed v=sqrt(T/u)

====>

v1/v2=sqrt(T1/T2)

if v2=2*v1

==> 1/2=sqrt(T1/T2)

==> T1/T2=1/4

==> T2=4*T1

tension required to change the factor of 4

2)

frequency, fn=n*V/2L

fundamental frequency, f1=v/2L

here,

if wave speed is doubled

==> fundamental frequency f1 also gets doubled

3)

tension, T1=2N

speed, v=sqrt(T/u)

===> v1/v2=sqrt(T1/T2)

if v2=2*v1

===>

v1/(2*v1)=sqrt(2/T2)

1/2=sqrt(2/T)

====> T2=8 N

tension T2=8 N

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