Experiment 11

STANDING WAVES ON A STRING

PRELAB

PURPOSE

To study wave motion and its superposition as exemplified by standing (stationary) waves on a vibrating string.

EQUIPMENT

tuning fork oscillator, pulley, string, mass holder and assorted masses, meter stick, thin paper strips.

RELEVANT FORMULAS

Wavelength-Frequency relation:              λ = v / f     or     v = f λ

Wave Speed on a String:                            

Distance between Adjacent Nodes:       λN = λ/2

DISCUSSION

The frequency of a wave is determined by the source of vibration. The wavelength depends on the speed of the wave, which is determined by the medium of propagation. Thus, for any wave:

λ = v / f                                                                                (1)

 

where λ is the wavelength (meters in SI units); v is the wave velocity (meters/sec); and f is the frequency (hertz). For transverse waves in a stretched cord having a tension T, it can be shown that:

                                                                                 (2)

 

where: v = wave velocity along the cord (m/s); T = tension (newtons) ; and, μ= linear mass density of the string =  (kg/m).

When two waves of equal frequency and amplitude propagate along a string in opposite directions, a special pattern of vibration is produced. This pattern appears to the naked eye to be standing still, hence the name "standing wave". Actually, the string vibrates rapidly in loops, which are separated by completely still points called Nodes. The middle of the vibrating loops are called Antinodes. The distance between adjacent Nodes is one-half of a wavelength, λ/2. By setting up a standing wave pattern, we have a simple method for determining the wavelength of the waves that are propagating. This technique can be used with any type of wave motion.

The apparatus for this experiment will allow you to set up transverse standing waves on a string. By eliminating v between Equations (1) and (2), we obtain a relation between quantities that are readily measurable: wavelength, frequency, and tension. The linear mass density μ, is a property specific to the string being used.

                                                                            (3)

 
 

Print out and complete the Prelab questions.