a piano string has a length of 2m and a density of 8,000kg/m3. when the tension in the string produces a strain of 1%, the fundamental note obtained is 170 Hz. calculate the modulus of elasticity for the material of the string.

Answer 1

f = sqrt (T/[m/L]) / 2L

m = 8000 A L
so
170 = sqrt (T/8000A)/4
680 = sqrt (T/8000A)

also
1% = .01 = T/ (E A)
so
T/A = .01 E

so
680 = sqrt (.01 E/8000)
462400 = .01 E/8000
E = 3.7 *10^11

Answer 2

This is not the formal solutiin though process is correct. Squrt should not be written it doesn't look good. Finally thanks for answer. I have done this but question bank answer was not matching. There may by mistake in qb.

Answer 3

A taut sonometer wire, 76 cm long, with a tension of 40 N is connected to a source of
alternating current. Two horse-shoe magnets of opposite poles are placed either side of the wire at its midpoint, and as current is allowed to pass through the sonometer, the resulting
forces set the wire in resonant vibration. If the density of the material of the wire is 8800 kg/m
3 and the wire is 1mm thick, obtain the frequency of the alternating current.