experiment: standing waves on a stringI need answers for the attached experiment questions and graph.

Standing Waves on a String

.

.

Objectives:

Demonstrate formation of standing waves on a string.

Determine the tension Ts of in the string required to produce standing waves.

Investigate the relationship between tension Ts and the wavelength 2.

• Determine an experimental value for the frequency f of the wave and compare it to the known

value of 60 Hz,

Equipment list:

String vibrator (f=60 Hz), string, clamps, pulley, hanger, slotted masses.

Overview: Waves on a string are an example of transversal waves. These are waves in which

individual particles of the medium (in this case the string) move perpendicular or transverse to energy

moving along the string. In Figure 1 a string tied to a vibrator at one end passes over a pulley, and the

weight of masses on the other end provides tension Ts in the string.

The vibrator moves up and down which produces a transversal wave that travel down the string.

The point where the string passes over a pulley is a fixed point and the wave is inverted by reflection at

this end, and travel back to the vibrator. Thus the string is a medium in which two waves of the same

speed, frequency and wavelength produce a standing wave. A standing wave, also known as a

stationary wave, is a wave that remains in a constant position. Its characteristic features are the

presence of loops, nodes and antinodes at points along the string. A node is a point on the string where

there is no displacement. A loop forms between 2 nodes. An antinode is a point for which the amplitude

is maximum. To form a standing wave, a node must occur at each end of the string, and an antinode

must occur between each node. The distance between nodes is N2, or one half of the wavelength. If

the length L of the string is measured, a standing wave has a wavelength of:

a=2L/n where n=number of loops (1, 2, 3, 4…)

(1)

node

antinode

loop

Length L

vibrator

M

Figure 1

Each standing wave corresponds to a different wave speed v. The wave speed is determined by the

tension in the string Ts and the string mass per unit length u known as a linear density of the string by

the equation:

T.

v=Vď

(2)

The wavelength 2 is in its stead determined by the frequency of the vibrator fand the wave speed by

the equation :

v=fa

(3)

Т.

Combining equations 2 and 3 gives:

A==

(4)

EXPERIMENTAL PROCEDURE:

1. The string mass per unit length should be determined by the class as a whole. Carefullymeasure 1 m

length of the type string to be used using a meter stick, cut it and measure the mass of this string ms to

the nearest Olg. From this data find linear density u=ms/length in kg/m and record it in

Table

your Data

2. Measure the length (using a tape measure or a meter stick) of the vibrating string from the tip of the

vibrator to the point where the string touches the pulley and record in the Data Table as string length L.

3. Plug in the vibrator and place masses on the hanger to produce 1 standing wave. This will be done by

adding and subtracting masses M until the loops with nodes and anti-nodes are clearly formed.

Record the value of mass (plus hanger) in your Data Table.

4. Continue the process of producing loops by removing mass to produce standing waves for 2, 3,

5,6, and 7 loops. Once you clearly see the loops stop and record the value of the mass M used to get

these loops in Data Table. To avoid searching at random, use eq. (4) above to have an indication of the

expected mass for each number of loops.

5. Use the measured string length L found at point 2 to calculate the wavelength à using the equation:

2 =2L/n

where n=number of loops ( 2, 3, 4…)

6. From the mass values M calculate the tension Ts=Mg with M in kg and g=9.80m/s?.

Record the values of Ts in

your

Data Table.

7. Calculate the values of VT, by taking the square root of the values found at 6 and record them in

your Data Table.

Lab Report

g/m =

kg/m

Mass of 1 m of string: p= 0.30

Length of the string L= 125.0

cm =

digit

m

4 digit

n

M (9)

M (kg)

Ts=Mg (N)

VT (VN)

a (cm)

2 (m)

1

2

3

4

650

170

80

42

27

18:5

12

65

. 17

.08

.042

027

, 185

-012

5

21

6

7

1. Using at least 75% of the graph paper, make a graph with a on Y axis and VT, on the X axis.

slu

2. Draw a best fit line (a line that doesn’t hit any data points but rather goes in between data points) and

calculate the slope by picking two points exactly on the best fit line, do not use data points to calculate

slope. Show your calculation on your graph to get credit.

Slope=

(unit:

3. Calculate the intercept

intercept=

(unit:

1

4. According to equation (4), a should be linearly proportional to VT, with

as a slope.

fra

1

Equate your slope to

and solve for the unknown frequency f.

fexp=

(unit:

)

4. Calculate and record the percentage error of fexp compared to the known value (standard) of

the frequency f-60 Hz.

% error =

Answer all questions:

1. Was the experiment accurate in finding the experimental value for the frequency? YES NO State

clearly the basis for your answer.

2. Was the experiment of finding the frequency precise? YES NO What would your need to answer this

question? Explain your reasoning.

3. Does the value of intercept you found reasonable? YES NO Explain your answer.

4. Suppose the frequency is f=60 Hz, L is the one you measured, and the string has a linear density

u=2.95 x 104kg/m. What is the tension Ts in the string for one loop? Show your work.

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