A piano tuner stretches a steel piano wire with a tension of 765 N.

Question

The steel wire has a length of 0.900m and a mass of 6.75g .? 

 

What is the frequency f1 of the string's fundamental mode of vibration? 

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?

 

Answer 1

(1)

The Tension in the String is 765 N.

Steel wire length L is 0.900 m

Mass of the string m is 6.75 g = 6.75 * 10^-3 kg.

Frequency of the string = n *(Velocity of the wave on the String/(2L) )

Velocity of the wave on the string

v = 319.37 m/sec

For Fundamental Frequency n = 1

Frequency = V / 2L

f = 319.37 / (2*0.9)

f = 177.42 Hz

Therefore Fundamental Frequency of the String is 177.42 Hz.

Answer 2

(2)

Frequency f = 16 kHz

Velocity of the wave on the string v = 319.37 m/sec

Frequency of the string f = n *(Velocity of the wave on the String v /(2L) )

n = f * (2L / v)

n = 16*10³ (2*0.9 / 319.37)

n = 90.17

n ≈ 90

The number of Harmonic is 90.