Help with Transverse Wave Equation

In summary, we have two vibrating sources emitting waves in the same elastic medium with frequencies of 25 Hz and 75 Hz, respectively. The first source has a wavelength of 6.0 m and reflects off a barrier at an angle of 25 degrees. The waves from the second source refract into a different medium at an angle of incidence of 35 degrees and a speed of 96 m/s. Using the universal wave equation V = (f)(L), we can find the speed and wavelength of the second source. However, there is not enough information given to solve for both variables, so we may need to use other equations or methods.
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Homework Statement



Two vibrating sources emit waves in the same elastic medium. The first source has a frequency of 25 Hz, while the 2nd source's frequency is 75 Hz. Waves from the first source have a wavelength of 6.0 m. They reflect from a barrier back into the original medium, with an angle of reflection of 25 degrees. Waves from the second source refract into a different medium with an angle of incidence of 35 degrees. The speed of the refracted wave is observed to be 96 m/s.

I need to find the speed of waves from the second source in the originial medium and if the angle of refraction of the waves from the second source are greater, less or equal to 35 degrees as they enter the different medium.


Homework Equations


The universal wave equation is V = (f)(L)
V = speed
f = frequency
L = wavelength

also f = 1/T
T = period (time) f anf t are reciprocals of each other

The Attempt at a Solution



Given: f = 75Hz
refracted v = 96m/s
angle of incidence = 35 degrees

Required: speed (v)
wavelength (L)

Analysis: V = (f)(L)
= (75)(?)

I just don't know how to find either the v or the L as this is the only formula I've been given and I can't use it with two variables. I tried making a graph with the angles but didn't have enough information. I don't know if I can somehow use the angles to calculate the refracted wave's original speed or if there's a way to use the refracted wave's speed to calculate the original speed. This is a grade eleven physics problem and I am so frustrated with this and can't see a way to solve it. If someone could even just help me find the wavelength of the second source that would help a lot.
 
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  • #2
Can anybody help with this?
 

1. What is the transverse wave equation?

The transverse wave equation is a mathematical formula that describes the motion of a transverse wave. It is given by the equation y = A sin(kx - ωt), where y is the displacement of the wave from its equilibrium position, A is the amplitude, k is the wave number, x is the position, ω is the angular frequency, and t is the time.

2. How do you solve the transverse wave equation?

To solve the transverse wave equation, you need to plug in the values of the variables (amplitude, wave number, angular frequency, position, and time) into the equation and then perform the necessary mathematical operations. The resulting value of y will give you the displacement of the wave at a specific point in space and time.

3. What is the significance of the transverse wave equation in physics?

The transverse wave equation is significant in physics because it allows us to mathematically describe the behavior of transverse waves. These types of waves are important in many areas of physics, such as electromagnetism, optics, and quantum mechanics.

4. Can the transverse wave equation be modified for different types of waves?

Yes, the transverse wave equation can be modified to describe different types of waves, such as longitudinal waves. For example, the equation y = A sin(kx - ωt) can be modified to y = A cos(kx - ωt) for longitudinal waves.

5. What is the relationship between the transverse wave equation and the speed of the wave?

The speed of a transverse wave is related to the angular frequency and the wave number through the equation v = ω/k. This means that as the angular frequency or the wave number increases, the speed of the wave also increases. Additionally, the amplitude of the wave does not affect its speed.

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