Introduction:

Waves exist in numerous forms, they are classified into two groups longitudinal waves and transverse waves. A wave down the length of a fixed string is a perfect example of a transverse wave. Where this wave has a speed of where the direction of motion of this wave is perpendicular to the direction of propagation of energy.

In a medium where a string is fixed at both ends, when a transverse wave is created the waves reaches the other end and then reflects back having the same speed but in opposite direction. This reflection results in the occurrence of a physical phenomena called standing waves.

A standing wave has points of zero displacement called antinodes these points mark the beginning and end of each loop in the standing wave. Where each loops has the value of half the wavelength of the wave. On the other hand there are also points of maximum displacement called antinodes where they are the amplitude of the standing wave. The mathematical representation of standing waves is a follows. Where The aim of my experiment is to prove that this equation is valid.

Method:
Apparatus:
String
Loud speaker
Masses 50-450g
Ruler
Pully
Clamp
Pipe
Scale

Attach the pipe to the table using the clamp, then set up the pulley and the string to the pipe using a different clamp. The string is passed through the pulley and attached to the loud speaker. Then we attach the masses to the string to create tension. And measure the length of the loops that are created. Finally weigh the spring and measure its length.
.

Data collected:

Table 1: experimental values
Mass (g)
Tension (N)
Loops Measured
Distance (cm)
Wavelength (cm)
50
0.497
5
160.3
64.12
100
0.981
3
136.6
91.07
150
1.472
3
170.0
113.3
200
1.962
2
134.0
134.0
250
2.453
2
144.8
144.8
300
2.943
1
80.7
161.4
350
3.433
1
86.6
173.2
400
3.924
1
91.3
182.6
450
4.415
1
94.8
189.6

Mass of spring:

Length of spring:

the linear density of the spring Is equal to :

= 0.003158( = 3.15×

to avoid the square root present in the standing wave equation I used the linearized equation from the lab manual given as:

Table2: wavelength squared values and tensions table 3:Linest values

slope m= 0.832 ± 0.022

y-intercept b= 0.0623 ±0.06

= = 3.0755
= 0.5 = 0.194

Analysis of the standing wave equation:

(Length) (Time) n=0.5

(Mass)m=-1

This means that the equation can be written in the following form:

Discussion:

The experiment had some assumptions, where the purpose of these assumptions was to avoid complex calculations and for better result accuracy. First of all we assumed that the pulley was frictionless. And the spring was ideal. Also for easier calculations it was assumed that the uncertainty