What is the wavelength of the sound waves?

In summary, the problem involves finding the wavelength of a sound wave based on the distance between the first and sixth nodes. The correct answer is 12.0 cm, and the solution involves counting the number of nodes between the first and sixth one and using the formula \frac{2}{5} L = \lambda to calculate the wavelength.
  • #1
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Homework Statement


a stationary sound wave has a series of nodes. The distance between the first and the sixth node is 30.0 cm. What is the wavelength of the sound waves?


Homework Equations





The Attempt at a Solution


well no idea about it
but in my attempt to solve it, i tried assuming 2L = [tex]\lambda[/tex]
but there are 6 nodes so [tex]\lambda[/tex] = [tex]\frac{1}{3}[/tex]L
by substituting the value of dist, i get [tex]\lambda[/tex] = 10cm
which is wrong. the ans is 12.0 cm
i wonder how to solve it
 
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  • #2


Try drawing yourself a diagram of the problem (ie just draw a wave going through six nodes), you should be able to solve it a bit more easily once you can visualise it.
 
  • #3


Your current working is neglecting the fact that there are two nodes at either end of this hypothetical wave. (kind of analogous to a similar problem you are probably familiar with - ie if a farmer had 100m of wire to build a fence and he could place the posts 2m apart, how many posts would he need?)
 
  • #4


i think i know it
probably i should count the between one
so it should be [tex]\frac{2}{5}[/tex] L = [tex]\lambda[/tex]
by computing it
i get 12.0 cm
yeah
thx all of you
 

What is the wavelength of the sound waves?

The wavelength of a sound wave is the distance between two consecutive points in the wave that are in phase. It is represented by the symbol λ (lambda) and is measured in meters (m).

How is the wavelength of sound waves related to frequency?

The wavelength and frequency of sound waves are inversely proportional. This means that as the frequency of a sound wave increases, the wavelength decreases, and vice versa.

What factors affect the wavelength of sound waves?

The wavelength of sound waves is affected by the speed of sound in the medium it is traveling through. It is also affected by the temperature, humidity, and density of the medium.

Can the wavelength of sound waves be changed?

Yes, the wavelength of a sound wave can be changed by altering the frequency or the speed of sound in the medium. This can be achieved by changing the properties of the medium, such as temperature or density, or by using different instruments or techniques to produce sound waves.

Why is the measurement of wavelength important in understanding sound waves?

The measurement of wavelength is important in understanding sound waves because it helps us to determine the characteristics of the sound, such as pitch and frequency. It also helps us to understand how sound behaves and how it can be manipulated in different environments.

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