H(n)=2n-1; find h(3y)

The speed of a wave depends on the characteristics of the medium. For example, in the case of a guitar, the strings vibrate to produce the sound. The speed of the waves on the strings, and the wavelength, determine the frequency of the sound produced. The strings on a guitar have different thickness but may be made of similar material. They have different linear densities, where the linear density is defined as the mass per length,

μ

=

mass of string

length of string

=

m

l

.

In this chapter, we consider only string with a constant linear density. If the linear density is constant, then the mass

(

Δ

m

)

of a small length of string

(

Δ

x

)

is

Δ

m

=

μ

Δ

x

.

For example, if the string has a length of 2.00 m and a mass of 0.06 kg, then the linear density is

μ

=

0.06

kg

2.00

m

=

0.03

kg

m

.

If a 1.00-mm section is cut from the string, the mass of the 1.00-mm length is

Δ

m

=

μ

Δ

x

=

(

0.03

kg

m

)

0.001

m

=

3.00

×

10

−

5

kg

.

The guitar also has a method to change the tension of the strings. The tension of the strings is adjusted by turning spindles, called the tuning pegs, around which the strings are wrapped. For the guitar, the linear density of the string and the tension in the string determine the speed of the waves in the string and the frequency of the sound produced is proportional to the wave speed.

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