# Sinusoidal Wave Frequency 500 Hz: Pi/3 Rad Apart

• bearhug
In summary, The sinusoidal wave has a frequency of 500 Hz and a speed of 350 m/s. To find the distance between two points that differ in phase by Pi/3 rad, the equation y= Asin(kx-wt+pi/3) was used. The wavelength was found to be 0.70m and k was calculated to be 8.98. The value of w was found to be 3141 using w=2pi/T, but the amplitude is unknown. Plugging in the values and solving for x will give the distance between the two points. Alternatively, the phase difference between two points that are a whole wavelength apart can also be found using this approach.
bearhug
A sinusoidal wave of frequency 500 Hz has a speed of 350 m/s.
(a) How far apart are two points that differ in phase by Pi/3 rad?

I was thinking that I need to use the equation y= Asin(kx-wt+pi/3)

I found the wavelength=0.70m

used this to find k=8.98

solved for w by converting the frequency to the period and using w=2pi/T to get w=3141 but I don't have amplitude.

I figured after plugging everything in and solving for x gives me the distnace apart. Is this the right approach?

What is the phase difference between two points that are a whole wavelength apart?

Yes, your approach is correct. To find the distance between two points that differ in phase by Pi/3 rad, you can use the equation y= Asin(kx-wt+pi/3) and solve for x. The value of x will give you the distance between the two points. You have correctly found the wavelength and the value of k. To find the value of w, you can use the equation w=2pi/T, where T is the period (1/frequency). Once you have the value of w, you can plug it into the equation and solve for x. This will give you the distance between the two points that differ in phase by Pi/3 rad.

## 1. What is a sinusoidal wave?

A sinusoidal wave is a type of wave that follows the shape of a sine function. It is characterized by a repeating pattern of crests and troughs, with a constant frequency and amplitude.

## 2. What is the frequency of a 500 Hz sinusoidal wave?

The frequency of a 500 Hz sinusoidal wave is 500 cycles per second, or 500 Hz. This means that the pattern of the wave repeats 500 times in one second.

## 3. What does "Pi/3 Rad Apart" mean in relation to the wave?

The phrase "Pi/3 Rad Apart" refers to the phase shift of the sinusoidal wave. It means that the wave is shifted in time by Pi/3 radians, which is approximately 60 degrees. This shift determines the starting point of the wave and can affect its shape.

## 4. How is the frequency of a sinusoidal wave related to its wavelength?

The frequency and wavelength of a sinusoidal wave are inversely related. This means that as the frequency increases, the wavelength decreases and vice versa. This relationship is described by the formula: wavelength = speed of wave / frequency.

## 5. What factors can affect the frequency of a sinusoidal wave?

The frequency of a sinusoidal wave can be affected by factors such as the medium through which it is traveling, the properties of the source creating the wave, and any external forces acting on the wave. For example, in a stringed instrument, the tension of the string and the length of the string can affect the frequency of the sound wave produced.

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