• anhnha
In summary: There is a sinusoidal voltage source at transmitter and speed of propagation for the wave is v (m/s), the direction in which the wave moves is z.Say, at t=0, the voltage at the source is 2V then at t=1s, at the point A that is v(m) away from the source in z direction, the voltage will be 2V, right?If you are looking at an oscilloscope your phase will repeat in time steps of T=period of the wave=1/f.In summary, the wave propagates at v (m/s) in the z direction. The voltage at the source is 2V at t=1s.

#### anhnha

Hi,
I want to ask one question about wavelength. Here is a picture defining wavelength.
To get a sinusoidal wave in space, we have to use a sinusoidal voltage source at transmitter, right?
I mean if there is a sinusoidal voltage source at the transmitter to create a sinusoidal wave in space.

#### Attachments

• wavelength.PNG
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Yes, where T is the period of the wave, f=1/T is the frequency, and lambda is the wavelength.

Note that wavelength x frequency = speed of propagation for the wave. This is the phase velocity.

Thank you, I wanted to know that to confirm my understanding about how wave propagating in space. For example,
there is a sinusoidal voltage source at transmitter and speed of propagation for the wave is v (m/s), the direction in which the wave moves is z.
Say, at t=0, the voltage at the source is 2V then at t=1s, at the point A that is v(m) away from the source in z direction, the voltage will be 2V, right?

If you are looking at an oscilloscope your phase will repeat in time steps of T=period of the wave=1/f.

Not sure what distance you are interested in here ...

I don't understand why the waveform in all wavelength are all sinusoidal. What shape of wave in space if the signal generated at transmitter is not sinusoidal? And then how we can definition wavelength in this case?

anhnha said:
I don't understand why the waveform in all wavelength are all sinusoidal. What shape of wave in space if the signal generated at transmitter is not sinusoidal? And then how we can definition wavelength in this case?

You could define terms like wavelength for a lot of non-sinusoidal waves, however there's a reason we usually focus on sinusoids. Fourier series/transform theory tells us that we can take any arbitrary wave and write it as a sum of sinusoidal waves. For example, a 2 Hz triangle wave can be written as a sum of 2 Hz, 4 Hz, 6 Hz, 8 Hz, etc. sinusoidal waves.

Rather than analyzing any arbitrary waveform (which may be messy and hard to understand), the easiest approach for a lot of problems is to break up an arbitrary non-sinusoidal waveform into sinusoidal components, analyze those components individually, and then add everything back up to get your result. It sounds like more work, but if you take a course on signal processing you'll quickly see the advantage. So basically, rather than study every kind of possible wave (assigning them wavelengths and what-not), we study sinusoids in great detail because we know that once we understand sinusoids, we can use that knowledge to understand a wide range of other types of waves.

Edit: by the way, you're right that a non-sinusoidal source would produce a non-sinusoidal wave. Your voice, for example, is a non-sinusoidal sound wave. However, like I explained above, it's usually much easier to describe your complicated vocal signal by breaking it down into sinusoidal waves rather than trying to analyze it directly.

Any wave has a period; you simply note when the wave repeats itself ...

But the simplest waveforms are sinusoids; you can build any wave from a collection of sinusoids - though it may take be a very large number, and sharp edges won't reproduce exactly.

anhnha said:
Thank you, I wanted to know that to confirm my understanding about how wave propagating in space. For example,
there is a sinusoidal voltage source at transmitter and speed of propagation for the wave is v (m/s), the direction in which the wave moves is z.
Say, at t=0, the voltage at the source is 2V then at t=1s, at the point A that is v(m) away from the source in z direction, the voltage will be 2V, right?

If you look at the signal that's producing the wave (say, the signal from a tone generator, fed to a loudspeaker, waggling a string - and not necessarily a sinusoid, say a sawtooth waveform or perhaps a square wave) with an oscilloscope, you cannot know the wavelength - only the variation of the volts with time. A freeze frame photo of the wave on the string would have a similar shape, only this time the variation would be with distance, rather than in time. You would not know the frequency from that picture; it will show the wavelength. The relationship between the frequency, seen on an oscilloscope (number of cycles per second) and the wavelength (spacing between similar points on the wave), multiplied together, will give you the speed of the wave. That's how frequency and wavelength relate to each other (the so called 'wave equation').

## What is wavelength?

Wavelength is the distance between two consecutive peaks or troughs of a wave. It is commonly denoted by the Greek letter lambda (λ) and is measured in meters (m) or nanometers (nm).

## How is wavelength related to frequency?

Wavelength and frequency are inversely proportional to each other. This means that as wavelength increases, frequency decreases and vice versa. The relationship between the two can be described by the equation: c = λν, where c is the speed of light, λ is the wavelength, and ν is the frequency.

## Why is understanding wavelength important?

Understanding wavelength is crucial in various fields of science, including physics, chemistry, and astronomy. It helps us understand the properties of waves and how they behave, which has practical applications in technologies such as telecommunications and medical imaging.

## How do we measure wavelength?

Wavelength can be measured using instruments such as rulers, calipers, and spectrometers. In the case of electromagnetic waves, wavelength can be calculated using the speed of light and frequency. For other types of waves, such as sound waves, wavelength can be measured directly using a ruler or calculated using the speed of sound and frequency.

## What factors can affect wavelength?

Wavelength can be affected by the medium through which a wave travels. For example, the wavelength of light changes when it passes through different mediums, such as air or water. Additionally, the source of the wave, such as an instrument or an object, can also affect its wavelength.