Question about travelling wave equation

In summary, the conversation discusses a multiple choice question about traveling waves and the resulting wave equation based on given parameters. The answer on the book is different due to an additional phase of pi, and the concept of amplitude is clarified to be a positive magnitude rather than a negative value.
  • #1
Yoseph Santoso
19
0
There is a multiple choices question about traveling wave in my book.
Based on the graphic, if T = 2s, the wave equation is ...

fis.jpg


My answer :
ω = 2π/T = 2π/2 = π
k = 2π/λ = 2π/4 = 0,5π → in my country, we use comma (,) for point (.)
y = ±A sin (ωt - kx)
y = -0,5 sin (πt - 0,5πx)
y = -0,5 sin π(t - 0,5x)

but the answer on my book is B. Could we throw the negative anyway?
 
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  • #2
Yoseph Santoso said:
There is a multiple choices question about traveling wave in my book.
Based on the graphic, if T = 2s, the wave equation is ...

View attachment 258146

My answer :
ω = 2π/T = 2π/2 = π
k = 2π/λ = 2π/4 = 0,5π → in my country, we use comma (,) for point (.)
y = ±A sin (ωt - kx)
y = -0,5 sin (πt - 0,5πx)
y = -0,5 sin π(t - 0,5x)

but the answer on my book is B. Could we throw the negative anyway?
You can't just throw away the negative, but you can see it's the same equation as B with an additional phase of ##\pi##.
 
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Likes Yoseph Santoso
  • #3
How do you get the minus sign?
 
  • #4
PeroK said:
You can't just throw away the negative, but you can see it's the same equation as B with an additional phase of ##\pi##.
Amplitude itself is just distance
It can't be negative.
 
  • #5
Adityameowmeow said:
Amplitude itself is just distance
It can't be negative.
Nobody was making the amplitude negative. If the equation is ##y=-A\sin(\omega t)##, where A>0, then the amplitude is A. Changing it to ##y=A\sin(\omega t)## would be wrong, but if you wish you can change it to ##y=A\sin(\omega t+\pi)##.
 
  • #6
Adityameowmeow said:
Amplitude itself is just distance
A better term in English is "magnitude". Just like a vector has "magnitude" and "direction". :smile:
 

Related to Question about travelling wave equation

What is the travelling wave equation?

The travelling wave equation is a mathematical representation of a wave that propagates through a medium. It describes the relationship between the displacement of the wave and its position and time.

What are the variables in the travelling wave equation?

The variables in the travelling wave equation are amplitude, wavelength, frequency, and velocity. Amplitude represents the maximum displacement of the wave, wavelength is the distance between two consecutive peaks or troughs, frequency is the number of complete cycles of the wave per unit time, and velocity is the speed at which the wave travels.

How is the travelling wave equation derived?

The travelling wave equation is derived from the wave equation, which is a partial differential equation that describes the behavior of a wave. By applying certain assumptions and simplifications, the wave equation can be reduced to the travelling wave equation.

What are the applications of the travelling wave equation?

The travelling wave equation has many practical applications in fields such as physics, engineering, and telecommunications. It is used to study and understand various types of waves, including electromagnetic waves, sound waves, and water waves. It is also used to design and analyze systems that involve the propagation of waves, such as antennas, musical instruments, and communication networks.

Can the travelling wave equation be used to describe all types of waves?

No, the travelling wave equation is only applicable to linear waves, which are waves that exhibit a linear relationship between their displacement and the restoring force. Non-linear waves, such as shock waves and solitons, require different equations to describe their behavior.

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