Question

A string with tension Ft= 10 N, with one end pinned and the other end free, is used to produce a wave supplied by a driving frequency. (a) If the frequency with which you produce waves is f= 10KHz and the wavelength of the wave is a = 0.01 m, what is the velocity with which the wave? (5 points) (b) What is the period of the wave? (5 points) (c) What is the linear mass density of the string? (5 points)

Answer 1

To solve the problem it is necessary to apply the theory of sine waves. The wavelength λ of a sinusoidal waveform traveling at constant speed v is given by

$\lambda = \frac{v}{f}$

Where,

v= velocity

f = frequency

Re-arrange to find v, we have

$v = f\lambda$

PART A ) Replacing with our values we have,

$v = (10*10^3)(0.01)$

$v = 100m/s$

PART B) In the case of the period we know that it is defined as a function of frequency as,

$T= \frac{1}{f}$

That is to say that using the previously given values we have that the period in seconds is,

$T=1*10^{-4}s$

PART C) Finally the transverse wave velocity is given by,

$v=\sqrt{\frac{T}{\mu}}$

Where,

T= Period

$\mu =$ Linear mass density

Re-arrange to find $\mu,$

$\mu = \frac{T}{v^2}$

$\mu = \frac{1*10^{-4}}{100^2}$

$\mu = 1*10^{-8}kg/m$