Laboratory 21\ Standing Waves on a String\ OBJECTIVES\ If a string is fixed at one end and attached to a sinusoidally driven vibrator at the other end, waves travel down the string from the vibrator and are reflected back from the fixed end. Under the proper conditions, standing waves are formed from the interference between the two waves traveling in opposite directions. The tension

T

in the string of length

L

, the mass per unit length of the string

p

, the frequency of the vibrator

f

, and the velocity of propagation of the waves

V

are the relevant variables of the problem. For a string of length

L

, measurements of the values of the tension

T

for which resonances occur will be used to accomplish the following objectives:\ Demonstration that resonances occur only for certain discrete values of the tension

T

in the string\ Determination of the value of the tension

T

required to produce resonances with a given number of nodes\ Determination of the wavelength

\\\\lambda

of the wave associated with a given resonance with a given number of nodes\ Demonstration that the wavelengths

\\\\lambda

associated with resonances are proportional to

\\\\sqrt(T)

, where

T

stands for the values of the tension in the string that produce resonances\ Determination of an experimental value for the frequency

f

from a linear least squares fit to the data for

\\\\lambda

versus

\\\\sqrt(T)

\ Comparison of the experimental value for the frequency with the known value of

120Hz

\ EQUIPMENT LIST\ String vibrator (

60HzAC

), string\ Clamps, pulley, support rods\ Mass holder and slotted masses\ Meter stick (preferably 2 -m stick)\ Laboratory balance capable of measuring to

0.00001kg

(one for the class)\ THEORY\ Waves are one means by which energy can be transported. Waves in a string are an example of a type of wave known as a transverse wave. The motion of the individual particles of the medium (in this case the string) move perpendicular or transverse to\ Laboratory 21\ 243

Laboratory 21 Standing Waves on a String OBJECTIVES If a string is fixed at one end and attached to a sinusoidally driven vibrator at the other end, waves travel down the string from the vibrator and are reflected back from the fixed end. Under the proper conditions, standing waves are formed from the interference between the two waves traveling in opposite directions. The tension T in the string of length L, the mass per unit length of the string p, the frequency of the vibrator f, and the velocity of propagation of the waves V are the relevant variables of the problem. For a string of length L, measurements of the values of the tension T for which resonances occur will be used to accomplish the following objectives: 1. Demonstration that resonances occur only for certain discrete values of the tension T in the string 2. Determination of the value of the tension T required to produce resonances with a given number of nodes 3. Determination of the wavelength of the wave associated with a given resonance with a given number of nodes 4. Demonstration that the wavelengths associated with resonances are proportional to T, where T stands for the values of the tension in the string that produce resonances 5. Determination of an experimental value for the frequency f from a linear least squares fit to the data for versus T 6. Comparison of the experimental value for the frequency with the known value of 120Hz EQUIPMENT LIST 1. String vibrator ( 60HzAC ), string 2. Clamps, pulley, support rods 3. Mass holder and slotted masses 4. Meter stick (preferably 2 -m stick) 5. Laboratory balance capable of measuring to 0.00001kg (one for the class) THEORY Waves are one means by which energy can be transported. Waves in a string are an example of a type of wave known as a transverse wave. The motion of the individual particles of the medium (in this case the string) move perpendicular or transverse to