How Many Oscillations Has This Wave Completed?

[hopelessphysics]

Homework Statement

A wave has a wavelength of 3.0m; a frequency of 25.0 Hz; and amplitude of 14.0 cm. The wave travels in the positive x-direction and has a value of zero at t=x=0. How many complete oscillations has the wave made at t= 20.0 s and x=4.2 m?

A) 3132
B) 1566
C) 498
D) 25
E) 3

Homework Equations

T=1/f

The Attempt at a Solution

Looking at the problem I was confused because if the wave length is 3m and the x distance after it stops is 4.2 meters, wouldn't it only complete one full oscillation?

 

[ehild]

You have to consider the phase of the wave, how many times 2pi is it.

 

[hopelessphysics]

what do you mean? what is the phase of the wave?

 

[NascentOxygen]

How many cycles are produced during that 20 second duration?

 

[hopelessphysics]

that would be the frequency times the time period? so 25×20?

 

[ehild]

what do you mean? what is the phase of the wave?

You write the wave as y=Asin(ωt-kx). The argument of the sine is the phase.

 

[NascentOxygen]

that would be the frequency times the time period? so 25×20?

So in 20 seconds, 25x20 cycles propagate outwards from the origin.

 

[hopelessphysics]

So 500 would be the answer?

 

[NascentOxygen]

So 500 would be the answer?

The answer to which question, exactly?

 

[hopelessphysics]

the original equation: How many complete oscillations has the wave made at t= 20.0 s and x=4.2 m?

 

[NascentOxygen]

the original equation: How many complete oscillations has the wave made at t= 20.0 s and x=4.2 m?

I can see how the 20 seconds is accounted for, but where have you taken into consideration that 4.2 meters?

 

[hopelessphysics]

thats what I am confused about

 

[hopelessphysics]

I don't understand how the two go together?

 

[NascentOxygen]

That 4.2m is your monitoring distance from the origin. The origin is the point where the waveform propagates from.

 

[hopelessphysics]

so how does it affect the 20×25?

 

[NascentOxygen]

You need to draw a diagram. A set of axes, with the wave originating at the origin and moving out along the x axis. Mark on it the 4.2 m.

 

[hopelessphysics]

How will that help me?

 

[andrevdh]

We can see from the problem that you are at the point in the course where you need to acquire this knowledge
This simulation might help, although here the wave is reflected back at the right hand end (select loose end ,oscillate and no damping):
https://phet.colorado.edu/en/simulation/wave-on-a-string

 

[ehild]

How will that help me?

You might consider to follow my method shown in Post #6 .

The wave is a function of both t (elapsed time) and x ( the distance traveled ) .
It can be written as y=A sin(ωt-kx) where ω is the angular frequency and k is the wavenumber. In terms of frequency f and wavelength λ, the wave is y=Asin[2π(f t - x/λ) ].
y = 0 when x = 0 and t = 0. A complete oscillation means that the phase 2π(f t - x/λ) changes by 2π and y returns to zero. You have to calculate how many times it happens till the given time and distance.