Physics 2025 – Lab 1 Standing Waves
Partner 1: Partner 2: Section:
Partner 3 (if applicable):
Standing Waves
Purpose:
Continuous waves traveling along a string are reflected when they arrive at the (in this case fixed) end of a string. The reflected wave interferes with the incoming wave, resulting in most cases in an erratic and irregular movement of the string. Under particular conditions (coordinated length of the string, wave frequency, linear mass density of the string, and tension of the string) a standing wave pattern emerges and can be observed very clearly. Under these conditions the wavelength of the standing wave (and thus that of the incoming wave) can be measured. The theoretical relationship between the aforementioned parameters is examined and tested for its consistency in a real experimental setting.
Apparatus List:
PASCO Mechanical Wave Miscellaneous Cables and Clamp and rod driver Adapters
Capstone Software Clamp and Pulley White Flexible String
Pasco Power Amplifier II Hooked weight set Digital Scale (on shared table) (CI-6552A)
Two C-Clamps Pasco 750 Interface
Theoretical Background
What Are Waves And How Can We Classify Them? In very general terms, a wave is a disturbance that travels from one place to another (for example, a stone thrown into a calm pond creates a disturbance that travels along the surface of the pond, away from the site of impact) . In addition, if the disturbance originates from a continuous source, then a continuous wave is created (for example, a wave created by a running motor of a boat). Furthermore, some waves are created by a continuous source that moves sinusoidally. The wave can then be classified as a harmonic wave. In this experiment we generate sinusoidal waves with the help of a computer, Capstone software, the 750 Pasco interface, and a Pasco amplifier. We will use sinusoidal waves in this experiment
5 Physics 2025 – Lab 1 Standing Waves because a sinusoidal (harmonic) wave has a distinct (single) frequency associated with it. In contrast, rectangular or saw-tooth waves are composed by superposition of many sinusoidal waves of different frequency and amplitude. Use of the harmonic waves therefore reduces greatly the number of parameters in our experiment. In other words, we can clearly identify the frequency of the wave by using harmonic waves.
Waves can be classified also by the direction of the disturbance. If the disturbance is perpendicular to the direction in which the wave travels, the wave is called “transverse” (an example would be a wave traveling along a string). If the disturbance is in the same direction as the direction in which the wave travels, the wave is called “longitudinal” (example: Sound).
Reflection of Waves, Standing Waves When a wave encounters a discontinuity of the medium in which it travels (sound hitting a wall, the end of a string, the water waves hitting the beach) a certain portion of the wave is reflected backwards. The pattern of the reflected wave resembles closely that of the incoming wave. In cases where the discontinuity forces the waves amplitude to be zero at the location of the discontinuity (e.g., when the end of a string is tied to a fixed place so its end cannot move) the reflected wave is inverted. In the opposite case (e.g., a string with a loose end that can move) the reflected wave is not inverted. In either case, if the wave is continuous, there will be basically two waves traveling simultaneously along the medium: The incoming wave and the reflected wave. The two waves will interfere, which means that their respective time and space dependent displacements will add up. In general, adding the incoming and reflected wave results in an irregular wave pattern. However, if the conditions are right, the interference results in a regular wave pattern along the medium. Such a regular pattern is called a standing wave.
The Speed Of A Wave Traveling On A String The speed (v) of a wave on a String is determined by two properties: 1) The tension (T) in the string. 2) The linear mass density of the string. The linear mass density can be calculated from the mass (m) of the string and it’s length (l):