Transverse Waves: Experiment
EXPERIMENT 5
TRANSVERSE STANDING WAVES
A string attached to a turning fork is set vibrating at the same frequency as the tuning fork. The length and tension in the string are adjusted until standing waves are observed on the string. By knowing the tension in the string and the wavelength of the standing waves, the frequency of oscillation of the string and thus, the tuning fork is found. This value is then compared to a strobelight determination of the frequency.
THEORY
If transverse waves of constant frequency and amplitude are sent down a string that is fixed at one end, then a reflection of the waves occurs and the oppositely directed waves interfere with each other to produce standing waves. A wave traveling in the positive x direction is given by
[pic] (1)
where A is the amplitude, k = 2[pic]/ [pic] with [pic] being the wavelength, and w= 2[pic]f with f being the frequency. For a similar wave traveling in the negative x direction with the same amplitude
[pic] (2)
If the amplitudes of the waves are small, then the waves obey the law of superposition and add linearly. The resultant wave is
[pic] (3)
which represents a standing wave whose amplitude, 2A cos wt is a function of time. Figure 1 shows the standing wave. The diagram indicates that the wave shape is not moving along the string but is only oscillating vertically on the string.
[pic]
Figure 1. A standing wave fixed at x = 0 and x = L. Five loops are shown.
The frequency of a wave is given by [pic] (4)
where V is the speed at which the transverse waves propagate along the string, The speed of the wave, in terms of the tension T, and the mass per unit length of the string [pic] is
[pic] (5)
The frequency is, therefore,
[pic] (6)
An alternate expression that can be used to calculate the frequency is
[pic] (7)
where L is the
TRANSVERSE STANDING WAVES
A string attached to a turning fork is set vibrating at the same frequency as the tuning fork. The length and tension in the string are adjusted until standing waves are observed on the string. By knowing the tension in the string and the wavelength of the standing waves, the frequency of oscillation of the string and thus, the tuning fork is found. This value is then compared to a strobelight determination of the frequency.
THEORY
If transverse waves of constant frequency and amplitude are sent down a string that is fixed at one end, then a reflection of the waves occurs and the oppositely directed waves interfere with each other to produce standing waves. A wave traveling in the positive x direction is given by
[pic] (1)
where A is the amplitude, k = 2[pic]/ [pic] with [pic] being the wavelength, and w= 2[pic]f with f being the frequency. For a similar wave traveling in the negative x direction with the same amplitude
[pic] (2)
If the amplitudes of the waves are small, then the waves obey the law of superposition and add linearly. The resultant wave is
[pic] (3)
which represents a standing wave whose amplitude, 2A cos wt is a function of time. Figure 1 shows the standing wave. The diagram indicates that the wave shape is not moving along the string but is only oscillating vertically on the string.
[pic]
Figure 1. A standing wave fixed at x = 0 and x = L. Five loops are shown.
The frequency of a wave is given by [pic] (4)
where V is the speed at which the transverse waves propagate along the string, The speed of the wave, in terms of the tension T, and the mass per unit length of the string [pic] is
[pic] (5)
The frequency is, therefore,
[pic] (6)
An alternate expression that can be used to calculate the frequency is
[pic] (7)
where L is the