Question
A wave traveling along the $x$ axis is described mathematically by the equation $y=0.17 \sin (8.2 \pi t+0.54 \pi x)$, where $y$ is the displacement (in meters), $t$ is in seconds, and $x$ is in meters. What is the speed of the wave?
Step 1
The general form of a wave equation is: y(x, t) = A sin(kx - ωt + φ) where A is the amplitude, k is the wave number, ω is the angular frequency, and φ is the phase constant. Comparing this general form with the given equation, we have: y(x, t) = 0.17 sin(8.2πt Show more…
Show all steps
Your feedback will help us improve your experience
Shoukat Ali and 101 other Physics 101 Mechanics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
$A$ traveling wave has displacement given by $y(x, t)=$ $(2.0 \mathrm{cm}) \times \cos (2 \pi x-4 \pi t),$ where $x$ is measured in $\mathrm{cm}$ and in s. a. Draw a snapshot graph of this wave at $t=0$ s. b. On the same set of axes, use a dotted line to show the snapshot graph of the wave at $t=1 / 8$ s. c. What is the speed of the wave?
The displacement (in meters) of a wave is given according to $y=0.26 \sin (\pi t-3.7 \pi x)$ where $t$ is in seconds and $x$ is in meters, (a) Is the wave traveling in the $+x$ or $-x$ direction? (b) What is the displacement $y$ when $t=38 \mathrm{~s}$ and $x=13 \mathrm{~m} ?$
A wave is represented by the equation $y=7 \sin \left(7 \pi t-0.04 x+\frac{\pi}{3}\right)$ where, $x$ is in metres and $t$ in seconds. The speed of the waves is (a) $(175 \pi) \mathrm{m} / \mathrm{s}$ (b) $(49 \pi) \mathrm{m} / \mathrm{s}$ (c) $(49 / \pi) \mathrm{m} / \mathrm{s}$ (d) $(0.28 \pi) \mathrm{m} / \mathrm{s}$
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD