Question

A 1.20 m wire has a mass of 6.80 g and is under a tension of 120 N. The wire is held rigidly at both ends and set into oscillation. (a) What is the speed of waves on the wire? What is the wavelength of the waves that produce (b) one-loop and (c) two-loop standing waves? What is the frequency of the waves that produce (d) one-loop and (e) two-loop standing waves?

Answer 1

Answer:

145.52137 m/s

1.4 m

0.7 m

60.6339 Hz

121.2678 Hz

Explanation:

T = Tension = 120 N

$\mu$ = Linear density  = $\frac{m}{L}$

m = Mass of wire = 6.8 g

L = Length of wire = 1.2 m

n = Number of loops

Velocity is given by

$v=\sqrt{\frac{T}{\mu}}\\\Rightarrow v=\sqrt{\frac{T}{\frac{m}{L}}}\\\Rightarrow v=\sqrt{\frac{120}{\frac{6.8\times 10^{-3}}{1.2}}}\\\Rightarrow v=145.52137\ m/s$

The speed of waves on the wire is 145.52137 m/s

Wavelength is given by

$\lambda=\frac{2L}{n}\\\Rightarrow \lambda=\frac{2\times 1.2}{1}\\\Rightarrow \lambda=1.4\ m$

The wavelength of the waves that produces one-loop standing waves is 1.4 m

$\lambda=\frac{2L}{n}\\\Rightarrow \lambda=\frac{2\times 1.2}{2}\\\Rightarrow \lambda=0.7\ m$

The wavelength of the waves that produces two-loop standing waves is 0.7 m

Frequency is given by

$f=\frac{nv}{2L}\\\Rightarrow f=\frac{1\times 145.52137}{2\times 1.2}\\\Rightarrow f=60.6339\ Hz$

The frequency of the waves that produces one-loop standing waves is 60.6339 Hz

$f=\frac{nv}{2L}\\\Rightarrow f=\frac{2\times 145.52137}{2\times 1.2}\\\Rightarrow f=121.2678\ Hz$

The frequency of the waves that produces two-loop standing waves is 121.2678 Hz