How Do You Calculate Transverse Wave Speed from a Wave Function?

AI Thread Summary
To calculate the transverse wave speed from the given wave function, focus on the relationship between displacement and time. The wave function provided is 15.0 cm cos(πx - 15πt), indicating that the wave speed is constant and does not depend on position. To find the transverse speed at a specific displacement of 12.0 cm, differentiate the wave function with respect to time, yielding the rate of change dy/dt. This approach simplifies the problem by eliminating the x-variable, allowing for a direct calculation of the transverse speed at the specified displacement. Understanding this relationship is key to solving the problem accurately.
newton10.3
Messages
2
Reaction score
0
I'm trying to calculate transverse wave speed for a point on a taut string when the y displacement is 12.0 cm. The given wave function is 15.0 cm cos(Pi*x-15Pi*t), and that is all I am given. How do you do this?
 
Physics news on Phys.org
Are you sure you're looking for the wave speed? It seems like the speed of the wave shouldn't depend on position in the string. Maybe you're looking for the speed of a point on the string?
 
That could be. The question states "What is the transverse speed for a point on a taut string" with the parameters I stated before.
 
Since wave speed doesn't depend on the x-position, you can zero it and remove it from the equation, then you are left with a simple: y= f(t) relationship.

Recalling some calculus and allowing me to rephrase the question should do the trick. What is the rate of change dy/dt when y is 12.
 

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Find transverse velocity given an equation of displacement
Replies
9
Views
2K
Waves and vibrations on a string
Replies
2
Views
2K
Conservation of power in a traveling wave on a string
Replies
9
Views
2K
Wave function - displacement - transverse wave
Replies
3
Views
2K
Question about Waves on a String
Replies
2
Views
2K
How Do You Calculate Max and Min Transverse Speeds in a Wave on a String?
Replies
1
Views
4K
Standing wave transverse motion and amplitude
Replies
5
Views
2K
How Do Phase Speed and Maximum Particle Speed Compare in a Transverse Wave?
Replies
5
Views
2K
How Do You Calculate the Propagation Speed of a Transverse Wave on a String?
Replies
8
Views
2K
Determining Parameters of a Transverse Harmonic Wave
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top