Question

A piano tuner stretches a steel piano wire with a tension of 765 N. The steel wire has a length of 0.800 m and a mass of 6.00 g.

1. What is the frequency f1 of the string's fundamental mode of vibration? (Express your answer numerically in hertz using three significant figures.)

=______ Hz


2.What is the number n of the highest harmonic that could be heard by a person who is capable of hearing frequencies up to f = 16 kHz?

n=_________________

Answer 1

v=frequency*wavelength

for fundamental frequency (first harmonic): wavelength=2L

v=(TL/m)^1/2

(765*.8/.006)^1/2=f*2*.8

f=200 Hz

Answer 2

tension on the wire T = 765 N

length of steel wire L = 0.8 m

mass of steel wire m = 6 g =0.006 kg

1) The fundamentalfrequency is

f = (1/2L)(T / (m/L))^1/2

=(1/2L)(L*T / m)^1/2
=( 1 / 2*0.8 ) ( 0.8*765 / 0.006) ^ ( 1/2)= 510.99 Hz2) Fromthe given datathe frequency n =16 Hz
The frequency with Pthhormonic isn p = (1/2L)(T /(m/L))^1/216P= (1/2L)(T / (m/L))^1/2= fnumber of loops p = 31.93= 31