How Do You Calculate Transverse Speed and Acceleration for a Wave on a String?

Therefore, the transverse speed at t = 0.150 s for the point on the string located at x = 1.60 m is 0.100 m * cos[(1.60/11 + 3*0.150)] = 0.00956 m/s. The acceleration can be found by taking the derivative of the transverse speed function, which is -0.100 m * sin[(1.60/11 + 3*0.150)] * (1/11) * 3 = -0.000140 m/s^2. In summary, the transverse speed at t = 0.150 s for the point on the string located at x = 1.60 m
  • #1
complexc25
12
0
A transverse wave on a string is described by the following wave function.
y = (0.100 m) sin [(x/11 + 3t)]
  • (a) Determine the transverse speed and acceleration at t = 0.150 s for the point on the string located at x = 1.60 m.
  • (b) What are the wavelength, period, and speed of propagation of this wave?
  • wrong check mark

I know that to find the transverse speed i need to find the derivative. I need a refresher on the derivative of that sin function, because I am getting the wrong answer. Once i get part A ill find out part B.
thanks in advance :redface:
 
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  • #2
The derivative of sin(x) is cos(x).
 
  • #3


Hello,

I can help you with this problem. Let's start with part A. To find the transverse speed, we need to take the derivative of the wave function with respect to time, which is given as:

y' = (0.100 m)(3)cos[(x/11 + 3t)]

Plugging in the given values, we get:

y'(1.60, 0.150) = (0.100 m)(3)cos[(1.60/11 + 3(0.150))] = 0.026 m/s

This is the transverse speed at t = 0.150 s for the point on the string located at x = 1.60 m.

To find the transverse acceleration, we need to take the second derivative of the wave function with respect to time, which is given as:

y'' = -(0.100 m)(3)^2sin[(x/11 + 3t)]

Plugging in the given values, we get:

y''(1.60, 0.150) = -(0.100 m)(3)^2sin[(1.60/11 + 3(0.150))] = -0.1 m/s^2

This is the transverse acceleration at t = 0.150 s for the point on the string located at x = 1.60 m.

Moving on to part B, the wavelength is given by the distance between two consecutive points on the string that have the same displacement and are in phase. In this case, it is the distance between two consecutive peaks or troughs of the wave. From the given wave function, we can see that the wavelength is 11 m.

The period is the time taken for one complete cycle of the wave. In this case, it is the time taken for the wave to travel one wavelength. From the wave function, we can see that the period is 3 seconds.

The speed of propagation is the speed at which the wave travels along the string. It is given by the product of wavelength and frequency. From the given wave function, we can see that the frequency is 1/3 Hz, so the speed of propagation is (11 m)(1/3 Hz) = 3.67 m/s.

I hope this helps. Let me know if you have any further questions. Good luck with your calculations!
 

Related to How Do You Calculate Transverse Speed and Acceleration for a Wave on a String?

1. What is a transverse wave?

A transverse wave is a type of wave in which the particles of the medium oscillate perpendicular to the direction of the wave's propagation. Examples of transverse waves include electromagnetic waves and surface water waves.

2. How do you calculate the wavelength of a transverse wave?

The wavelength of a transverse wave can be calculated by dividing the speed of the wave by its frequency. This can be represented by the equation λ = v/f, where λ is the wavelength, v is the speed of the wave, and f is the frequency.

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

A transverse wave is characterized by particles oscillating perpendicular to the direction of the wave's propagation, while a longitudinal wave is characterized by particles oscillating parallel to the direction of the wave's propagation. Sound waves are an example of longitudinal waves, while light waves are an example of transverse waves.

4. How does the amplitude of a transverse wave affect its energy?

The amplitude of a transverse wave is directly proportional to its energy. This means that as the amplitude increases, the energy of the wave also increases. This can be seen in ocean waves, where larger waves have more energy and can cause more damage.

5. What are some real-life applications of transverse waves?

Transverse waves have many practical applications, including communication technologies like radio, television, and cell phones. They are also used in medical imaging techniques like ultrasound and in various industrial processes such as welding and cutting. Additionally, transverse waves are important in the study of earthquakes, as they are responsible for producing the seismic waves that are measured to determine the magnitude of an earthquake.

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