Answer to Question #178283 in Mechanics | Relativity for Cornelius Abel

Question

The wave function of a standing wave is defined as y (x,t)=(4.44mm)sin {(0.0340rad/cm)}×sin {(754rad/s)t}

For two travelling waves that make up this standing wave.

Find:

(a) The amplitude?

(b) wavelength?

(c) Frequency?

(d) Wavespeed?

(e) Wave functions?

(f) From the given information, can you determine which harmonic this is? Explain your answer.

Answer 1

Answers

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a. amplitude = $\boxed{4.44\over 2}$

= 2.22mm

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b. $\boxed{ V = f \lambda}$

$\lambda$ = ${754\over 0.340 }\times{ 1\over 100}$ $\times$ $2\pi \over 754$

$\boxed{\lambda}$ = $\boxed{2π\over 34}$

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c. $\boxed{\omega = 2\pi{f}}$ = 754

$\implies$

$\boxed f$ = $\boxed{754\over 2\pi}$

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d. $\boxed V$ = $\boxed{\omega \over\kappa}$

V = $754\over 0.340$ $cm/s$

$\boxed V$ = $\boxed{{754\over 0.340 }\times{ 1\over 100}}$ m/s

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e.

We use $\boxed {2sinAsinB = cos(A-B)-cos(A+B)}$

On comparing we got

$\boxed {2.22[2sin(0.0340x)cos(754t)]}$

On solving we got

First function- $\boxed {2.22cos(0.0340x-754t)}$

second function $\boxed {- [2.22cos(0.0340x+754t)]}$

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f.

No$\implies$ length of the function is not given