Frequency and Period of a Wave
Calculate the amplitude and period of a sine or cosine curve. .. Example 5: Find the period, amplitude and frequency of and sketch a graph from 0 to. were given the frequency and asked to find the period using the following relationship. The Relationship between Wave Frequency, Period, Wavelength, and Velocity Figure Because they travel at the same speed in a given medium. Put the constants together with the integral and divide by one period to get the We now have an equation that relates intensity (I) to displacement amplitude (∆s). .. sound has a level of 0 dB at a pressure intensity of 20 μPa and frequency of.
Period refers to the time it takes something to happen. Frequency is a rate quantity.
Period is a time quantity. As an example of the distinction and the relatedness of frequency and period, consider a woodpecker that drums upon a tree at a periodic rate.
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If the woodpecker drums upon a tree 2 times in one second, then the frequency is 2 Hz. Each drum must endure for one-half a second, so the period is 0. If the woodpecker drums upon a tree 4 times in one second, then the frequency is 4 Hz; each drum must endure for one-fourth a second, so the period is 0.
If the woodpecker drums upon a tree 5 times in one second, then the frequency is 5 Hz; each drum must endure for one-fifth a second, so the period is 0. Do you observe the relationship?
Frequency and Period of a Wave
Mathematically, the period is the reciprocal of the frequency and vice versa. In equation form, this is expressed as follows.
Since the symbol f is used for frequency and the symbol T is used for period, these equations are also expressed as: The quantity frequency is also confused with the quantity speed.
The speed of an object refers to how fast an object is moving and is usually expressed as the distance traveled per time of travel.
For a wave, the speed is the distance traveled by a given point on the wave such as a crest in a given period of time. So while wave frequency refers to the number of cycles occurring per second, wave speed refers to the meters traveled per second.
A wave can vibrate back and forth very frequently, yet have a small speed; and a wave can vibrate back and forth with a low frequency, yet have a high speed. Frequency and speed are distinctly different quantities. Wave speed will be discussed in more detail later in this lesson. How do changes in the frequency of a wave affect the wavelength of a wave?
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Use the Wave plotter widget below to find out. Alter the frequency and observe how the pattern changes. We Would Like to Suggest The acceleration amplitude is the maximum change in acceleration. Amplitudes associated with changes in bulk properties of arbitrarily small regions of the medium The pressure amplitude is the maximum change in pressure the maximum gauge pressure.
The density amplitude is the maximum change in density. Measuring displacement might as well be impossible. For typical sound waves, the maximum displacement of the molecules in the air is only a hundred or a thousand times larger than the molecules themselves — and what technologies are there for tracking individual molecules anyway? The velocity and acceleration changes caused by a sound wave are equally hard to measure in the particles that make up the medium.
Density fluctuations are minuscule and short lived. The period of a sound wave is typically measured in milliseconds. There are some optical techniques that make it possible to image the intense compressions are rarefactions associated with shock waves in air, but these are not the kinds of sounds we deal with in our everyday lives.Using the Wave Equation (Wavelength, Speed and Frequency)
Pressure fluctuations caused by sound waves are much easier to measure. Animals including humans have been doing it for several hundred million years with devices called ears. Humans have also been doing it electromechanically for about a hundred years with devices called microphones.
All types of amplitudes are equally valid for describing sound waves mathematically, but pressure amplitudes are the one we humans have the closest connection to. In any case, the results of such measurements are rarely ever reported.
Instead, amplitude measurements are almost always used as the raw data in some computation.