Two sinusoidal waves of the same period

In summary, two sinusoidal waves of the same period have the same frequency and duration for one complete cycle. The period of a sinusoidal wave can be determined by calculating the time for one complete cycle. When two sinusoidal waves of the same period interfere, they can constructively or destructively interfere, resulting in a new wave with different characteristics. These waves can be used in practical applications such as sound and light waves. The difference between two waves of the same period and two waves of the same frequency is that the former have the same duration while the latter have the same number of cycles per second, and their amplitudes may differ.
  • #1
kukulalalu89
8
0
Two sinusoidal waves, identical except for phase, travel in the same direction along a string and interfere to produce a resultant wave given by

y(x,t)=(2.5 mm)sin(26.0x -4.0 s-1 * t+0.400 rad),

with x in meters and t in seconds.

1.) What is the wavelength of the two waves (m)? [I already solved this]

2.) What is the phase difference between them (radians, so enter no unit)?

3.) What is their amplitude (mm)?


Please HELP on #2 and #3!
 
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  • #2
Show your work.
 
  • #3
for number 1,

y =Asin(kx-wt)

k = 2∏/λ

k = 26

so λ = 2∏/26 = wavelength = 0.242 m.

But I'm having problems with 2 and 3.
 
  • #4
Show work for #2 and #3.
 

FAQ: Two sinusoidal waves of the same period

What is the definition of "Two sinusoidal waves of the same period"?

Two sinusoidal waves of the same period refers to two waves that have the same duration for one complete cycle. This means that both waves have the same frequency, or number of cycles per second, and therefore repeat their pattern at the same rate.

How can you determine the period of a sinusoidal wave?

The period of a sinusoidal wave can be determined by calculating the time it takes for one complete cycle to occur. This can be done by measuring the distance between two consecutive points on the wave that are at the same point in their cycle (e.g. two peaks or two troughs) and dividing by the wave's velocity.

What happens when two sinusoidal waves of the same period interfere with each other?

When two sinusoidal waves of the same period interfere with each other, they can either constructively interfere (amplitudes add) or destructively interfere (amplitudes cancel out) depending on their relative phase. This can result in a new wave with a different amplitude and phase.

How can two sinusoidal waves of the same period be used in practical applications?

Two sinusoidal waves of the same period can be used in practical applications such as sound and light waves. In sound, two waves may be combined to produce a new sound with different characteristics. In light, interference between two waves can create patterns such as diffraction grating.

What is the difference between two sinusoidal waves of the same period and two waves of the same frequency?

Two sinusoidal waves of the same period have the same duration for one complete cycle, while two waves of the same frequency have the same number of cycles per second. This means that while their periods may be the same, their wavelengths may differ. Additionally, two waves of the same frequency can have different amplitudes, while two sinusoidal waves of the same period have the same amplitude.

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