Question about travelling wave equation

[Yoseph Santoso]

There is a multiple choices question about traveling wave in my book.
Based on the graphic, if T = 2s, the wave equation is ...

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?

 

[PeroK]

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 $\pi$.

 

[nasu]

How do you get the minus sign?

 

[Adityameowmeow]

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.

 

[haruspex]

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 $y=A\sin(\omega t+\pi)$.

 

[berkeman]

Amplitude itself is just distance

A better term in English is "magnitude". Just like a vector has "magnitude" and "direction".