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In this lab you will study standing waves on a string. First you will measure the frequency of the normal modes at a constant tension. Next you will measure the frequency of a single harmonic at different tensions. In each case you can use these measurements to calculate the mass per unit length of the string. For traveling waves on a string the velocity v is equal to the square root of the tension over the mass per unit length of the string. We can also express the velocity as the product at the frequency and the wavelength. The wavelength is the linear distance for the wave to repeat, and the frequency is the number of times the wave repeats per unit time. For transverse waves the wave propagates in a direction perpendicular to the motion of the particles in the medium. Standing waves are created at resonant frequencies. At these frequencies the incoming and reflected wave add constructively to create a standing wave. Different resonant frequencies are called harmonics. We label each harmonic with a number n. The stationary points on the standing wave are called nodes, here marked in red. The points of maximum amplitudes are called anti-nodes. The harmonic number n is equal to the number of anti-nodes. Combining our earlier equations for the velocity of waves on a string, we find that the frequency is equal to 1 over the wavelength times the square root of the tension over the mass per unit length. For each harmonic the wave length is equal to two times the length of the string divided by n. Combining the above equations, we find an expression for the frequency of the nth harmonic in terms of the length of the string, the tension, and the mass per unit length of the string. To start the experiment first measure the mass per unit length of the string using a triple beam balance and the meter stick. Tie the string to the blue metal piece on speaker and thread it through the white plastic piece in the center. Connect the red and black cables to the speaker, then connect these cables to the power amplifier and connect the amplifier to the Pasco interface. Next clamp the metal bridge to the table with the fully Stretch the string across the table over the metal bridge and hang weights from the string. You can change the tension on the string by changing the amount of mass. To control the power amplifier with Data Studio select Channel A, and then choose power amplifier. A dialog box called signal generator will open. Here you can select the wave shape, the frequency, and the amplitude. Choose sine wave for the wave shape. When adjusting the amplitude do not that it above 5 volts. You can change the frequency and amplitude while their power amplifier is on by pressing the plus and minus buttons. You can also set the step size of these changes using a left and right arrows. Starting at 0 Hz, sweep through a range of frequencies to find a harmonic. These frequencies will have the largest amplitudes. This is the first harmonic, it has one anti-node in...
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