Superpositon and Standing Waves problem

In summary, the child's ear canal is 1.3 cm long and the question is asking for sound frequencies in the audible range that will result in increased hearing sensitivity. The formula used is f= m(v/4L) and the frequencies found were 6600Hz and 2.0*10^4Hz using m=1 and 3, respectively. The audible range typically goes up to 20000Hz.
  • #1
weezer13578
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Homework Statement


A child has an ear canal that is 1.3 cm long. At what sound frequencies in the audible range will the child have increased hearing sensitivity?


Homework Equations


for open-closed tube, f= m(v/4L)


The Attempt at a Solution


I need two frequencies since the question is asking for a rage in which the child has increased hearing sensitivity. So I thought for an open-closed tube, I could use f= m(v/4L) where m=1 and 3. But my answer does not work. How do I know what nodes (m) to choose? Please help.
 
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  • #2
I have previously found 6600 and 2.0*10^4 using m=1 and 3, and this range didn't work.
Could anyone help?
 
  • #3
The question is asking for specific frequecies in the audible range; not a range of frequencies.
The method is correct. 6600Hz is in the audible range (quarter wavelength). The next resonance should be at 3 times that value. (3/4 wavelength)
Audible range goes up to 20000Hz typically.
 

1. What is superposition and how does it relate to standing waves?

Superposition is the principle that states when two or more waves meet, they combine to form a new wave. This is relevant to standing waves because they are created by the superposition of two waves with the same frequency and amplitude traveling in opposite directions.

2. What is the difference between a node and an antinode in a standing wave?

A node is a point on a standing wave where there is no displacement or amplitude. An antinode, on the other hand, is a point on the standing wave where the displacement and amplitude are at their maximum. In other words, a node is where the wave is at its lowest point, and an antinode is where the wave is at its highest point.

3. How do the wavelength and frequency of a standing wave relate to each other?

The wavelength and frequency of a standing wave are inversely proportional. This means that as the frequency increases, the wavelength decreases, and vice versa. This relationship is governed by the equation λ = 2L/n, where λ is the wavelength, L is the length of the medium, and n is the number of nodes.

4. Can standing waves exist in all types of media?

Yes, standing waves can exist in any medium, as long as there are boundaries that reflect the waves back and create interference. This can occur in solid, liquid, and gaseous media, as well as electromagnetic waves in a vacuum.

5. How can standing waves be used in real-world applications?

Standing waves have many practical applications, such as in musical instruments, where they create distinct notes or harmonics. They are also used in industrial settings to detect flaws in materials through ultrasonic testing. Standing waves are also utilized in medical imaging techniques, such as ultrasound, to create images of internal body structures.

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