Question

A string has a linear density of 8.5 x 10-3 kg/m and is under a tension of 280 N. The string is 1.8 m long, is fixed at both ends, and is vibrating in the standing wave pattern shown in the drawing. Determine the
a. speed.
b. wavelength
c. frequency of the traveling waves that make up the standing wave.

Answer 1

Answer:

a)  $v=181.497m/s$

b)  $\lambda=1.2$

c)  $F=151.248hz$

Explanation:

From the question we are told that:

Linear density $\rho=8.5 x 10-3 kg/m$

Tension $T= 280 N$

Length of string $l= 1.8 m$

a)

Generally the equation for Speed of travelling wave is mathematically given by

 $v=\sqrt{\frac{T}{\rho}}$

 $v=\sqrt{\frac{280}{8.5*10^{-3}}$

 $v=181.497m/s$

b)

From the Drawing

Wavelength is given as

 $\lambda=\frac{2L}{3}$

 $\lambda=\frac{2*1.8}{3}$

 $\lambda=1.2$

c)

Generally the equation for Frequency of travelling wave is mathematically given by

 $F=\frac[v}{\lambda}$

 $F=\frac[181.497}{1.2}$

 $F=151.248hz$