Question

i need help with part B

Vibrating String Experiment Objective To study the factors affecting the velocity of waves in a stretched string Apparatus Linear transducer, function generator, string, meter stick, muss set, table clamp with pulley. Optional: strobe light, Part A Attach one end of a string to the motor and pass the other end of the string over a pulley about 1.5 m away. Set the frequency to 120 Hz. Refer to the figure below to make sure the orientation of the motor is correct Set the frequency generator amplitude to the 9 o'clock position (about 30% maximum). Do not set the frequency generator amplitude above 30% or else the transducer might drift around the table top. Set the hanging ma to 50 , and adjust the frequency until you get a 1 wavelength pattern with maximum amplitude. Repent this procedure, adding 50 grams to the hanger each time, up to a maximum of 300 g. Record the data in the table below. (Note that the masses jump from 200 g to 300 g in the last trial.) Trial 1 2 3 .150 Mass (kg) (H) TN) velocity (m/s) quared .050 16.31 16.31 49 266.02 .100 22.64 512.5 27.55 27.55 142 759,00 200 3179 31.791.96 1010.60 38.94 38,94 1516.32 Plot a graph of a vs. T. We can rewrite our equation for the speed of the wave: ²1.7 5 -300 The slope of the graph should be 1/1. Compare the two values of, the one obtained from the graph and the other from weighing the string on a balance and dividing by the length of the string. ass of string() Length (m) # (from slope) (masa/length) Percent difference .00 1839 1.524 1.953x10.00121 38%

Answer 1

Here we just use the simple formula for wavelength and velocity , solving for wavelength we have to be careful for taking value of n i.e normal mode.

For n=1 there is 2 nodes because of two ends and so on

We can calculate for 3,4and 5 nodes

Formula for warelength the 24 Lism normal mode V there Nodes Frequency (Hz) 2 For there is a nodes 3 nodes wavelength (on) velocity (oups (3) x12 3 52-29 nr 2 57.87 5842 58.61 n! 19:43 38.58 58.42 78.15 3 y 1 S n.3) nou, 0.75 1 d- velocity wareleyth velocity = (d) x(") = using uppes values for a nodes vs 3X19.43 = 58.29 similarly for others shown in Table Average velocity 58:29 + 57.97 +57.42 +59.61 Vexp 233.19 58.29 m/s u Uth = JT/u m=300g L=1.5m M = 0.00121 Kg/m [uppertable] Vtha ma 300 x 10°3x9.8 0.00121 $2429-75 49-29 m/s I uth Vexplk too y echor - Vh 149.29-58.291 x 100 49.29 49.29 18.25 %, verp (m/s) Vith (m/s) "%error 58.29 49.29 18.25 9 x100