How Do You Calculate the Speed and Deflection of a Wave on a String?

In summary, the conversation involves a request for help with understanding the mathematical description of a wave, specifically a transverse wave on a string. The conversation includes a request for finding the maximum transverse speed of a particle on the string and whether it is equal to the propagation speed of the wave. Additionally, there is a question about the frequency and deflection of a particle at a specific time and position for a wave with given amplitude, wavelength, and speed. The conversation ends with a playful hint to consult a textbook for help.
  • #1
saksham
16
0
Help Needed! Waves, Urgent!

******Mathematical description of a wave:******

A transverse wave on a string can be described by:
Y(x,t)= A cos [k(x-vt)]

a) Find the maximum transverse speed vy of a particle of the string. Under that circumstances is it equal to the propagation speed of the wave?

b) The wave has an amplitude of 0.300 cm, wavelength 12.0 cm, and speed 6.00 cm/s. What is its frequency? What is the deflection of a particle of the string at time t = 5 s and position x = 10 cm?

Please help me out! I have deadline tonight.

Physicist.
 
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  • #2
Hint for a: Find the transverse speed by taking the derivative.

Hint for b: Use the wave equation: [itex]v = f \lambda[/itex].

Hint for both: Crack open that textbook! :smile:
 
  • #3
Under what circumstances are the traverse speed and speed of propagation equal?
 

1. How is a wave mathematically described?

A wave can be mathematically described using the wave equation, which relates the properties of the wave (such as amplitude, wavelength, and frequency) to the medium it is traveling through.

2. What is the difference between a transverse and longitudinal wave?

A transverse wave is one in which the particles of the medium move perpendicular to the direction of wave propagation, while in a longitudinal wave, the particles move parallel to the direction of wave propagation.

3. How do you calculate the amplitude of a wave?

The amplitude of a wave is the maximum displacement of a particle from its equilibrium position. It can be calculated by measuring the distance between the highest point of a wave (crest) and the lowest point (trough).

4. What is the relationship between frequency and wavelength in a wave?

The frequency of a wave is the number of complete cycles it makes in one second, while the wavelength is the distance between two consecutive crests or troughs. The two are inversely proportional, meaning as frequency increases, wavelength decreases, and vice versa.

5. How does the speed of a wave relate to its frequency and wavelength?

The speed of a wave is determined by the frequency and wavelength. It can be calculated by multiplying the frequency by the wavelength, or by using the wave equation v = λf, where v is the speed, λ is the wavelength, and f is the frequency.

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