1a given a wave produced by a simple harmonic oscillator...

a. Given a wave produced by a simple harmonic oscillator whose displacement in meters is given by the equation [ y = 0.3cos(24πt)], what is the frequency of the wave in Hz? b. A tube of air open at only one end is vibrating in the 5th harmonic from a tuning fork of frequency 75 Hz placed at the open end. If this tube of air were to vibrate at its fundamental frequency, what frequency, in Hz, tuning fork would be needed at the open end? c. A 0.50-meter-long spring is stretched from its equilibrium position to a length of 1.00 meter by a weight. If 20 joules of energy are stored in the stretched spring, what is the value of the spring constant in N/m? d. A periodic transverse wave has an amplitude of 0.20 meter and a wavelength of 3.0 meters. If the frequency of this wave is 12 Hz, what is its speed?

Transcript

00:01 So this post has four different parts to this problem, and each part is a different concept.

00:09 So this first part gives us the equation of the position of a wave as y equals 0 .3 cosine of 24 pi times t.

00:19 Our goal is to find the frequency of this wave.

00:22 So in general, the wave equation is the amplitude times the cosine of omega -t, t so the angular frequency times t and if there's a phase shift we can add on plus fee but there is no phase shift so we don't have to worry about adding anything onto that so here's the general form of the wave equation so based on the problem omega is 24 times pi and this is helpful because there's a relationship between the angular frequency and the frequency so if we look at that relationship as the frequency equals the angular frequency divided by 2 pi, then we just have to substitute in 24 pi for omega and solve for the frequency.

01:12 So omega is 24 pi divided by 2 pi.

01:18 The pies cancel out.

01:20 24 divided by 2 gives us a frequency of 12 hertz.

01:26 That should be the answer to part a.

01:28 For part b, it says for an error column, who's...

01:34 For the nth harmonic, we get a wave produced from 75 hertz.

01:42 Our goal is to find what the fundamental frequency is or the frequency of the first harmonic.

01:48 So with waves in an air column, so there's a relationship between the harmonic number and the fundamental frequency.

02:01 So if we have the frequency of the nth harmonic, so any harmonic number, and we know for a closed air column, it has to be odd, we can find that if we multiply the harmonic number by the fundamental frequency, that gets us the frequency of any harmonic.

02:22 So for this problem, the frequency of the fifth harmonic is 75, the fifth n is 5 for the nth harmonic, and we can use this relationship to figure out what the frequency of the first harmonic is or the fundamental frequency.

02:41 So we just take 75, the frequency of the fifth harmonic, divided by 5, and we can get the frequency of the first harmonic is 15 hertz.

02:58 Part c says to find the spring constant when we do 20 joules worth of work to stretch a 0 .5 .1 .4...

Question

Please give Ace some feedback