Homework answers / question archive / PHYS 2426 Engineering Physics II Standing Waves Equipment Mechanical Vibrator Function Generator Mass Hanger Weights Plastic Spacer Aluminum Rod Pulley with Clamp C-Clamp String Ruler Figure 1 Overview In this lab you will explore the properties of standing waves generated on a string

PHYS 2426 Engineering Physics II Standing Waves Equipment Mechanical Vibrator Function Generator Mass Hanger Weights Plastic Spacer Aluminum Rod Pulley with Clamp C-Clamp String Ruler Figure 1 Overview In this lab you will explore the properties of standing waves generated on a string

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PHYS 2426 Engineering Physics II Standing Waves Equipment Mechanical Vibrator Function Generator Mass Hanger Weights Plastic Spacer Aluminum Rod Pulley with Clamp C-Clamp String Ruler Figure 1 Overview In this lab you will explore the properties of standing waves generated on a string. Standing waves are produced when a condition of resonance exists between the natural frequencies of the string and the frequency of the disturbance. In this lab, the string will be fixed at both ends so a standing wave must have a node at each end. As a result, standing waves are produced only at frequencies that produce integral numbers of halfwavelengths that fit into the length of the string. Theory The wavelengths ? are related to the frequency f of the disturbance and the velocity v of the wave on the string by the following equation: v ?? f Equation 1 The velocity of a wave on a string is given by the following equation: ?? v? FT ? Equation 2 where ? is the linear mass density of our physics string. FT is the tension force in the ?? string given by: FT ? Mg ?? Equation 3 Procedure In this experiment the cord used is highly elastic, and the linear mass density ? will have to be calculated for each different amount of tension force. Here is how it is done: The elastic cord has a mass density ?0 = 3.95×10-3 kg/m when relaxed. You will find two brightly colored marks separated by some distance in the middle of your cord. The mass of string between these marks is 1.0 gram =1.0×10-3 kg. So, for each case where the tension is different you must calculate the corresponding linear mass density using the equation ? ? m / L , where m is the mass between the marks (1.0×10-3 kg), and L is the (new, stretched) distance between the marks. Be sure to use the correct ? value for each tension case in the data table below, and record the value of ? in the table. After the lab assistant sets up the apparatus, begin the lab. Vary the frequency and/or tension for various waves and number of antinodes and record in the table. The table on the next page has room for you to record the data for five different scenarios. Keep the voltage applied to the wave driver less than or equal to 3 volts max, and use hanging weights and cord lengths that give 3 or more antinodes in the oscillating portion of the cord. Measure the half-wavelength between consecutive nodes in the middle of the oscillating portion of the cord. The hanging masses should be limited to a maximum of 200 grams, including the 50 gram hanger. In the final column of the table you will calculate the percent difference between your predicted (calculated) frequency and the frequency actually applied by the function generator. Use the following formula: %_ Difference ? | f calculated ? f applied | *100 f applied