Question

EXAMPLE 8.7 string 4.0 m long has a mass of 3.0 g. One end of the string is fasted to a stop and the other end hangs over a pulley with a 20 kg mass attached. What is the speed of a transverse wave in this string?​

Answer 1

Answer:

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

Answer 2

The speed of a transverse wave in this string is 511.5 m/s.

Given:

Length of string: 4 m

Mass of string: 3 g

Mass of pulley: 20 Kg

To find:

The speed of a transverse wave in this string.

Solution:

We know:

v = √(T/μ)

v = $\sqrt{MgL/m}$

Here,

M = 20 Kg

g = 9.8 m/s²

L = 4 m

m = 3 gm or 0.003 Kg

and string's mass per unit length is denoted by μ

Putting the values in equation:

v = $\sqrt{(20) (9.8) (4)/(0.003)}$

v = 511.5 m/s

Therefore, the speed of the transverse wave in the string is 511.5 m/s