Waves, finding frequency, wavelength, and speed

In summary, the displacement of a wave traveling in the negative y-direction can be represented by the equation D(y,t)=(5.2cm)sin(5.5y+72t). To find the frequency, wavelength, and speed of the wave, we can use the equation D(x,t) = A sin[2π (x/λ -t/T) + Φ], where 5.5 = 2π/λ. This allows us to easily find the wavelength. By understanding the relationship between frequency and period, we can also find the frequency. And by using the relationship between frequency, wavelength, and velocity, we can find the speed of the wave.
  • #1
aliaze1
174
1
I am assigned the even problem for homework, but I am lost, so I found an odd problem with the same type of question and has the answer... I just need to know how the calculations are done

Homework Statement



The displacement of a wave traveling in the negative y-direction is D(y,t)=(5.2cm)sin(5.5y+72t), where y is in m and t is in sec. Find the frequency, wavelength and speed of the wave

Homework Equations



D(x,t) = A sin[2π (x/λ -t/T) + Φ]

The Attempt at a Solution



I have no clue, the answers are:

11.5 Hz
1.14 m
13.1 m/s
 
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  • #2
Well I'll help get you started.

By comparing the two equations, you know that

[tex]5.5 = \frac{2\pi}{\lambda}[/tex]

So you can easily find the wavelength.

How can you find the frequency in a similar manner? What is the relationship between frequency and period? When you have the frequency and wavelength, what is the relationship between those and velocity?
 
  • #3
Thanks!
 
Last edited:

1. What is a wave?

A wave is a disturbance that travels through space and time, transferring energy from one point to another without permanently displacing the medium (such as air or water) through which it travels.

2. How do you find the frequency of a wave?

The frequency of a wave is the number of complete cycles the wave makes in one second. It can be calculated by dividing the speed of the wave by its wavelength.

3. What is the relationship between frequency, wavelength, and speed?

The frequency of a wave is inversely proportional to its wavelength, meaning that as the frequency increases, the wavelength decreases. The speed of a wave is directly proportional to its frequency and wavelength, meaning that as the frequency increases, the speed also increases.

4. How do you measure the wavelength of a wave?

The wavelength of a wave can be measured by finding the distance between two consecutive points on the wave that are in phase, or in other words, have the same position and are moving in the same direction.

5. Why is it important to understand waves and their properties?

Understanding waves and their properties is crucial in various fields such as physics, engineering, and medicine. Waves play a significant role in communication, energy transfer, and many natural phenomena. By understanding waves, we can manipulate and utilize them for various purposes.

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