Question

help on #3 and #4 please

show all work

3. A string with a mass per unit length of 3.4 x 10-**. is attached to a string vibrator (frequency = 120 Hz) with a string extended over a pulley with mass hanging on the string (like in our lab). The length of the vibrating portion the string (between the string vibrator and the pulley) is 75 cm. Calculate the mass that would need to be hong the string in order to observe the first and second harmonic standing waves. 4. An organ pipe is 38 cm long and is open at both ends. Determine the fundamental frequency when T-28°C.

Answer 1

3 Given mass pen unit rength M = 3.48104 frequency = 120 12 length of vibraton l = 75cm = 0.75 m The harmonic freauency ecuation is fe consider both ends ) for of the tension on the string is given by vast The mass that would be hung on the string for 1st &. and harmonie is given by, m= Me = 3.4810 kg x 0.75m = 2.95 x 104 uy = 0.255 gm (ons)

An ongan pipe of length p = 38CM = 0.38m The speed of sound in ain with ro temperature dependence is given by, V= (331-5 +0.6 m m At T328*C ; V=(331.5 + 0.6x204) en is V = (331.57 16-8) Mis - 348 mis for open is at bath ends, frequency Now fože fundamental frequency (n=1), on f = 348 mis on J ax 0:38.0 fe usq.951=457.9 Hz (wy).