Find the lowest frequency where the receiver is a node

[Physicsisfun2005]

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?

 

[Andrew Mason]

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:

$$\Delta d = n\frac{\lambda}{2}$$

$$\lambda = \frac{2\Delta d}{n}$$

So what is the maximum wavelength? From that and the wave equation $v = \lambda f$ 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

 

[Dr.Brain]

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.