As can be known from Eq.(2),the Young modulus of the sample rod under different temperature can be calculated by measuring its natural frequency f and other mechanical parameters under these temperatures.The measurement can be carried out using the setup shown in Figure 1. In this experiment,only the Young modulus at room temperature is measured,so the heating oven is not needed. Caution:Two problems need special attention! 1.The f in Eg.(2)which calculates the Young modulus is the fundamental frequency of the transverse vibration of the rod,which needs to be estimated during the experiment. 频率计 讯号 发生器 放大器 示波器 换能器 悬丝 测试棒 热电偶 ^ 200 电势 差计 电热丝 加热炉 Figure 1 Experimental setup for the measurement of Young modulus 2.It can be seen from Figure 1 that the exciting and detecting of the transverse vibration of sample rod is connected with the transducer by suspension fiber.If the connecting points are not at the wave nodes of the transverse vibration,the equation of the transverse vibration will not be satisfied.If the connecting points are at the wave nodes,then the vibration of the sample cannot be excited or detected.Hence in order to measure the natural frequency,normally the epitaxial method can be used to calculate the natural frequency.The details are as following:Accord ing to the solution of Eq.(1),the two wave nodes of the transverse vibration of the sample rod is at 0.224 I and 0.776 1,respectively,as shown in Figure 2. y◆ 0.5001 0.2247 0.7761x Figure 2 Position of the two key wave nodes for the epitaxial method (a)Firstly,connect the exciting and detecting suspension fibers at the positions 0.1/and 0.9/of the sample rod,respectively,looking for its resonance frequency fi. (b)Both two suspension fibers are then gradually pushed to the rod center withAs can be known from Eq. (2), the Young modulus of the sample rod under different temperature can be calculated by measuring its natural frequency f and other mechanical parameters under these temperatures. The measurement can be carried out using the setup shown in Figure 1. In this experiment, only the Young modulus at room temperature is measured, so the heating oven is not needed. Caution: Two problems need special attention! 1. The f in Eq. (2) which calculates the Young modulus is the fundamental frequency of the transverse vibration of the rod, which needs to be estimated during the experiment. 频率计 讯 号 发生器 放大器 示波器 电 势 差 计 热电偶 换能器 加热炉 悬丝 测试棒 电热丝 200V 图 (1) 2. It can be seen from Figure 1 that the exciting and detecting of the transverse vibration of sample rod is connected with the transducer by suspension fiber. If the connecting points are not at the wave nodes of the transverse vibration, the equation of the transverse vibration will not be satisfied. If the connecting points are at the wave nodes, then the vibration of the sample cannot be excited or detected. Hence in order to measure the natural frequency，normally the epitaxial method can be used to calculate the natural frequency。The details are as following：According to the solution of Eq. (1), the two wave nodes of the transverse vibration of the sample rod is at 0.224 l and 0.776 l, respectively, as shown in Figure 2. 0.500 l 0.224 l 0.776 l y O x 图 (2) (a) Firstly, connect the exciting and detecting suspension fibers at the positions 0.1l and 0.9l of the sample rod, respectively, looking for its resonance frequency f1. (b) Both two suspension fibers are then gradually pushed to the rod center with Figure 1 Experimental setup for the measurement of Young modulus Figure 2 Position of the two key wave nodes for the epitaxial method