# But, as a webpage title: Wave Problem: Solving for Phase Shift

• freezer
In summary, the amplitude is 6, the period is 250ms, the radian frequency is 8π rad/sec, and the phase is -8π/125 radians. The frequency is 4Hz and the phase in degrees is 5.76 degrees.
freezer

## Homework Statement

1. A signal of the form x(t) = A cos(ω0t + φ) is plotted below. From the plot, deduce the following:
(a) the amplitude A, (b) the period T0, (c) the radian frequency ω0, and (d) the phase φ in radians. For part (e), find f0 in Hz by converting the radian frequency from part (c). For part (f), convert the phase from part (d) to degrees.

## The Attempt at a Solution

a) Amplitude = 6 (inspection)
b) Period = (218.75ms + (-31.25ms)) = 250ms
c) ω=2π/T = 2π / 0.250s = 8π rad/sec
d) dφ=2π/dt = -8π/125
e) frequency = ω/2π = 8π/2π = 4Hz
f) deg = 180 φ/2π = 5.76 deg

y(t) = 6cos(8πt - 8π/125)

So i am not sure on my calculation for the phase shift.

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• Quest 1 Wave.png
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freezer said:

## Homework Statement

1. A signal of the form x(t) = A cos(ω0t + φ) is plotted below. From the plot, deduce the following:
(a) the amplitude A, (b) the period T0, (c) the radian frequency ω0, and (d) the phase φ in radians. For part (e), find f0 in Hz by converting the radian frequency from part (c). For part (f), convert the phase from part (d) to degrees.

## The Attempt at a Solution

a) Amplitude = 6 (inspection)
b) Period = (218.75ms + (-31.25ms)) = 250ms
c) ω=2π/T = 2π / 0.250s = 8π rad/sec
d) dφ=2π/dt = -8π/125
e) frequency = ω/2π = 8π/2π = 4Hz
f) deg = 180 φ/2π = 5.76 deg

y(t) = 6cos(8πt - 8π/125)

So i am not sure on my calculation for the phase shift.

## The Attempt at a Solution

It is a typo in b) (period) but the result is correct. The "+" should be "-".

As for the phase constant: The signal has the form Acos(ωt+φ) It is maximum when ωt+φ=0, or integer times 2pi. Nearest to t=0, there is a maximum at t=-31.25 ms. Take ωt+φ=0, and substitute -31.25 for t.

ehild

Last edited:
freezer said:

## Homework Statement

1. A signal of the form x(t) = A cos(ω0t + φ) is plotted below. From the plot, deduce the following:
(a) the amplitude A, (b) the period T0, (c) the radian frequency ω0, and (d) the phase φ in radians. For part (e), find f0 in Hz by converting the radian frequency from part (c). For part (f), convert the phase from part (d) to degrees.

d) dφ=2π/dt = -8π/125 QUOTE]

What's this?
From the graph, we have 6cos(0.1ω0 + φ) = -6.
Solve for φ.

## What is a phase shift in a wave problem?

A phase shift in a wave problem refers to the change in the position or timing of a wave compared to another wave. It can also be described as the difference in phase between two waves.

## How is a phase shift represented in a wave?

A phase shift is typically represented by a shift in the horizontal position of a wave on a graph. This can also be visualized as a change in the starting point of the wave or a shift in the wave's peaks and troughs.

## What causes a phase shift in a wave?

A phase shift in a wave can be caused by a change in the wave's frequency, velocity, or medium. It can also be caused by interference from other waves or reflections.

## What are some real-life examples of phase shifts in waves?

Phase shifts can be observed in many natural phenomena, such as sound waves traveling through different mediums, electromagnetic waves passing through different materials, and ocean waves encountering different depths or currents.

## How do scientists use phase shifts in their research?

Scientists use phase shifts in various fields of study, including physics, engineering, and astronomy. They can use phase shifts to analyze and measure the properties of waves, such as their frequency, wavelength, and amplitude. They can also use phase shifts to study the behavior and interaction of different waves.

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