Find the lowest frequency where the receiver is a node

In summary, the problem involves two loud speakers 2.5m apart and a receiver 3m from one speaker and 3.5m from the other. The task is to find the lowest frequency where the receiver is a node and the number of nodal lines. The formula used to find the wavelength is X/L=n(lambda)/d. However, the question can also be answered by finding the maximum wavelength using the formula v = lambda f. The number of nodal lines can be determined by calculating the angle between nodes.
  • #1
our teacher gave us this one in class and its not one of the "regular" ones we do so i same not sure how to set it up w/o getting messy numbers.

2 loud speakers 2.5m apart and a reciever 3m from one speaker and 3.5m from the other.

a. find the lowest frequency where the receiver is a node

b. # of nodal lines

to get the wavelength in order to find the frequency for (a.) do i just use the relationship X/L=n(lambda)/d?
 
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  • #2
Physicsisfun2005 said:
our teacher gave us this one in class and its not one of the "regular" ones we do so i same not sure how to set it up w/o getting messy numbers.

2 loud speakers 2.5m apart and a reciever 3m from one speaker and 3.5m from the other.

a. find the lowest frequency where the receiver is a node

b. # of nodal lines

to get the wavelength in order to find the frequency for (a.) do i just use the relationship X/L=n(lambda)/d
This is analagous to double slit diffraction for light. The sound waves from the two speakers interfere and create a pattern of loud, soft areas along a 'screen line'.

But I think the question can be answered more easily than by using a diffraction pattern formula. A node occurs where the difference in the distance of the receiver from speaker1 to speaker2 has to be 1/2 a wavelength. So:

[tex]\Delta d = n\frac{\lambda}{2}[/tex]

[tex]\lambda = \frac{2\Delta d}{n}[/tex]

So what is the maximum wavelength? From that and the wave equation [itex]v = \lambda f[/itex] you can work out the frequency.

The number of nodal lines depends on wavelength. Can you work out the angle between nodes by working out the distance the next node would be from the receiver?

AM
 
  • #3
Imagine the two speakers as two ends of a rope in which the wave is travelling.Now you know that for this kind of a rope , the relation is given by:

L=n(wavelength)/2

Also distance between two nodes or antinodes is always equal to (wavelength/2)

according to your question L=2.5m

You can calculate wavelength as per given distance of nodes, which will give you the value of n which will be the lowest.
 

What is the concept of "Find the lowest frequency where the receiver is a node"?

"Find the lowest frequency where the receiver is a node" refers to a process in which the receiver, which is a device used to receive signals, is also used as a node in a network to transmit signals. This concept is often used in wireless communication systems.

Why is it important to find the lowest frequency where the receiver is a node?

Finding the lowest frequency where the receiver is a node is important because it allows for efficient use of the available frequency spectrum. By using the lowest possible frequency, the receiver can avoid interference from other signals and achieve a stronger and more reliable connection.

What factors affect the lowest frequency where the receiver is a node?

The lowest frequency where the receiver is a node can be affected by various factors such as the distance between the transmitter and receiver, the type of antenna used, and the presence of obstacles or interference in the surrounding environment. These factors can impact the signal strength and quality, which in turn affects the lowest frequency that can be used.

How is the lowest frequency where the receiver is a node determined?

The lowest frequency where the receiver is a node is determined through a process called frequency planning. This involves analyzing the characteristics of the wireless network, including the number of nodes, their locations, and the desired coverage area. By considering these factors, the optimal frequency can be selected for each receiver to ensure the best possible performance.

What are the benefits of using the lowest frequency where the receiver is a node?

Using the lowest frequency where the receiver is a node offers several benefits, including increased range and coverage, reduced interference, and improved signal quality. It also allows for more efficient use of the available frequency spectrum, which can be especially beneficial in crowded or high-demand environments.

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