(3) The lowest note on a piano (the first harmonic vibration) is the "A" note, which has a frequency of 27.5 Hz. The entire string is 2.0 m long and has a mass of 402 g. The vibrating section of the string is 1.89 m long. (a) What tension is required to tune the string properly? (answer: 2170 N) (b) What is the wavelength of the first harmonic vibration? (answer: 3.78 m) (c) What are the wavelength and frequency of the second harmonic vibration of the string? (answer: 55.0 Hz and 1.89 m) (d) What are the wavelength and frequency of the fourth harmonic vibration of the string? (answer: 110 Hz and 0.945 m) 2L F fn = 2L n

(a) Determine the transverse speed at t= 0.230 s for an element of the string located at x= 1.50 m? {b) Determine the transverse acceleration at t = 0.220 s for an element of the string located at x = 1.50 m ? Step 2 5 Solution in y = 0.09 sinl 12 at F=0,2305ec and x= 15m U= (0:09) [5T)Cos(is +5xx-) > N= -1.91 m/seel ) 16/=1141m/sec (b) a-dv = -(0.09 x (25n²) sincui0o6) ) la = 1-5498 m/sec}

P 18-28 page-559 Refer to the figure below where the attached mass m hangs from a cord around a pulley, with m= 5.00 kg. The length of the cord between point P and the pulley is L = 2.00 m. The vibrator is set to a frequency of 150 Hz and a standing wave of six loops is formed, as shown in the figure above. (a) Determine the linear mass density of the string. (b) How many loops (if any) will result if the mass m is changed to 45 kg? (c) How many loops (if any) will result if the mass m is changed to 10 kg?