What is the frequency of the wave?

In summary, the conversation discusses a sound wave traveling at 345 m/s through air in a long horizontal tube. At a specific instant, two air molecules at different positions have different displacements, and the frequency of the wave is being sought. The formula s = sm cos(kx - ωt + φ) is used, where s represents displacement, sm is the maximum displacement, k is the wave number, x is the position, ω is the angular frequency, t is time, and φ is the phase angle. However, to find the frequency, the value of a is needed, which is not present in the equation.
  • #1
FearlessRose
8
1
1.
A sound wave of the form s = sm cos(kx - ωt + φ) travels at 345 m/s through air in a long horizontal tube. At one instant, air molecule A at x = 2.00 m is at its maximum positive displacement of 6.30 nm and air molecule B at x = 2.09 m is at a positive displacement of 2.40 nm. All the molecules between A and B are at intermediate displacements. What is the frequency of the wave?
Here is what I've gotten so far.
s=6.30 nm at 2m
s=240nm at 2.09
since s is max at 2m, the sm=6.40nm

s=smcos(kx-wt+phi)
kx-wt + phi=acos(s/sm)

I have everything I need but, how do I find out what the value of a is?
 
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  • #2
There is no a, acos stands for arccos(y), the inverse cosine function.
 
  • #3
Thank you!
 

FAQ: What is the frequency of the wave?

1. What is the definition of frequency in relation to waves?

The frequency of a wave is defined as the number of complete cycles of the wave that occur in one second. It is measured in Hertz (Hz) or cycles per second.

2. How is frequency related to the energy of a wave?

The frequency of a wave is directly proportional to its energy. This means that as the frequency increases, the energy of the wave also increases. This relationship is described by the equation E = hf, where E is energy, h is Planck's constant, and f is frequency.

3. What factors affect the frequency of a wave?

The frequency of a wave is determined by the source of the wave and the medium through which it travels. The type of source, such as a vibrating string or electromagnetic radiation, and the properties of the medium, such as density and elasticity, can affect the frequency of the wave.

4. What is the relationship between frequency and wavelength?

The frequency and wavelength of a wave are inversely proportional to each other. This means that as the frequency increases, the wavelength decreases, and vice versa. The relationship is described by the equation c = λf, where c is the speed of the wave, λ is wavelength, and f is frequency.

5. How is frequency measured in different types of waves?

In electromagnetic waves, frequency is measured in Hertz (Hz), while in mechanical waves, such as sound waves, it is measured in cycles per second or Hertz. In seismic waves, frequency is measured in oscillations per second.

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