Question

A certain vibrating string on a piano has a length of 74 cm and forms a standing wave having two antinodes.  

(a) Which harmonic does this wave represent?

(b)  Determine the wavelength of this wave

(c) how many nodes are there if 20.0 Newton find the fundamental frequency I'm the next three frequencies that could cause standing wave patterns on the street

Answer 1

Given,

Length of string L=74cm

Number of Antinode=2

(A) Since the wave has two antinode So The wave is in second harmonic.

(B) Wavelength $\lambda=\dfrac{2L}{n}=\dfrac{2\times 74}{2}=74cm$

(C) There are 3 nodes there.

Tension in he string T=20N

Mass per unit length $\mu=9\times 10^{-3}kg/m^3$

Velocity of wave $\nu=\sqrt{\dfrac{T}{\mu}=}\sqrt{\dfrac{20}{9\times 10^-3}}=47.14m/s$

Fundamental frequency $f_1=\dfrac{v}{2l}=\dfrac{47.14}{2\times 0.74}=31.85Hz$

Next three frequencies are $2f_1,3f_1,4f_1=63.70Hz,95.55Hz,127.40Hz$