Lab #3: Vibrating Strings- Standing waves in a string.
In this lab, you will study the transverse standing waves formed along a vibrating string attached to a tuning fork. The tuning fork vibrates up and down creating transverse standing wave patterns along the string length between the tuning fork and the pulley. The string is connected to hanging weight through a pulley to adjust tension
As you already know, “transverse” indicates that the displacement of the wave medium (the string) from equilibrium is perpendicular to the direction of propagation of the wave (which is parallel to the string). “Standing” indicates that the waves do not appear to be moving in either direction; rather, a seemingly stationary pattern appears due to constructive and destructive interference of two counter-propagating waves. Hence, the anti-nodes (the “maxima” in the amplitude of transverse oscillations) and the nodes (the “minima” in the amplitude of transverse oscillations) do not move. These transverse standing waves will only appear under certain conditions, which is what you will investigate in this lab.
In this lab, a standing wave pattern is produced by a tuning fork that vibrates one end of the string up and down. As this happens, the string displacement is sent from one end of the string to the other. At this other end, which is fixed, the incoming wave reflects and bounces back in the other direction. When it reaches the end with the motor, it is reflected back, and this repeats again and again. However, if the reflected wave traveling to the left is in phase with the original wave traveling to the left, then their amplitudes constructively interfere. Similarly, the leftward moving wave and a rightward moving wave may interfere destructively. The combination of all of these interactions yields a standing wave pattern, as shown in the diagram below, which looks like a stationary wave pattern, rather than many separate waves traveling to the left and to the right. Depending on the speed of the electric motor, different frequencies can be generated along the length of the string, so long as there are nodes at the two fixed endpoints.
n=number of loops4th harmonic
The equation for the velocity of these counter-propagating waves along the string is:
Where v is the speed, T= tension and µ is the mass per unit length.
In this lab, you will first predict what the traveling wave velocity v should be for a string, using the stretched linear mass density μ of the string and the tension T along the string due to a hanging mass M. Next, you will excite multiple orders (labeled as “order n”) of standing waves along the string.
Go to the simulation
Change linear mass density, µ, tension T, frequency f to obtain required number of loops. Use table below to compare experimental and theoretical values of speed of standing waves along the string.
Number of loops n
Mas per unit length µ
In your conclusion, discuss your results. How close were the two velocity values you? If they are very different give any possible reasons.