Two loudspeakers emit waves, find wavelength

In summary, the conversation discusses the use of the formula Δ∅=2π (Δx/λ) +Δ∅0 =(m) 2π to find the wavelength of sound waves emitted by two loudspeakers. The first person used the formula and manipulated it to solve for λ=0.4m, while the second person suggested simply measuring the distance between two points of maximum sound intensity to find the wavelength. The first person's approach was confirmed to be correct by the second person.
  • #1
Moolisa
20
5
I solved it, but then saw another solution online and am wondering if is is correct (since it is much faster than mine) and if my reasoning of it is correct

1. Homework Statement

Two loudspeakers emit sound waves along the x-axis. A listener in front of both speakers hears a maximum sound intensity when speaker 2 (s2) at origin and speaker 1 (S1) at x = 0.50 m. If s1 slowly moved forward, the sound intensity decreases, then increases, reaching another maximum when s1 is at x = 0.90 m.
a. What is wavelength

Homework Equations


Δ∅=2π (Δx/λ) +Δ∅0 =(m) 2π

The Attempt at a Solution


My Solution[/B]
I used Δ∅=2π (Δx/λ) +Δ∅0 =(m) 2π
I let m=1 when Δx=0.5m for equation 1 and m=0 when Δx=0.9m for equation 2. I manipulated they equations so each equaled Δ∅0 and then set equations 1 and 2 equal to each other. Then I solved for λ=0.4m

Person Online
They just measured the two distances between maximum sound intensities in order to get wavelength. Now this makes sense to me (I think...) since it is essentially just measuring the distance between two crests. Is this reasoning wrong?More detailed version of my attempt
1st situation, m=1, Δxa=0.5m
Δ∅=2π (Δxa/λ) +Δ∅0 =2π (1)
I manipulated the equation so
Δ∅0=2π (1-(Δxa/λ)) Equation 1

2nd Situation, m=0, Δxb=0.9m
Δ∅=2π (Δxb/λ) +Δ∅0=2π (0)
Δ∅0= -2π (Δxb/λ) Equation 2

Then I set 1 and 2 equal to another and got wavelength

 
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  • #2
Your approach is correct. Look what happens when you manipulate those equations.
$$2\pi[1 - (\Delta x_a/\lambda) ]= -2\pi(\Delta x_b/\lambda)$$
$$1 - (\Delta x_a/\lambda) = -\Delta x_b/\lambda$$
$$1 = \frac {\Delta x_a - \Delta x_b} {\lambda}$$
$$\lambda = \Delta x_a - \Delta x_b$$

The difference between the two positions is one wavelength. Just as the other solution said.
 
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Related to Two loudspeakers emit waves, find wavelength

What is the concept of two loudspeakers emitting waves?

The concept of two loudspeakers emitting waves is based on the principles of sound waves. When two loudspeakers emit sound waves, they interact with each other and create a phenomenon known as interference. This interference can result in changes in the amplitude and wavelength of the waves being emitted.

What is the relationship between the wavelength and frequency of the waves emitted by two loudspeakers?

The wavelength and frequency of the waves emitted by two loudspeakers are inversely proportional. This means that as the frequency increases, the wavelength decreases, and vice versa. In other words, when the frequency of the waves emitted by the loudspeakers increases, the distance between two consecutive wave crests decreases.

How can the wavelength of the waves emitted by two loudspeakers be determined?

The wavelength of the waves emitted by two loudspeakers can be determined by using the formula λ = v/f, where λ is the wavelength, v is the speed of the waves (which is usually the speed of sound in air), and f is the frequency of the waves. This formula is based on the relationship between wavelength and frequency mentioned earlier.

What is the difference between constructive and destructive interference in the context of two loudspeakers emitting waves?

Constructive interference occurs when the waves emitted by two loudspeakers are in phase (i.e. their crests and troughs align), resulting in an increase in the amplitude of the waves. On the other hand, destructive interference occurs when the waves are out of phase, resulting in a decrease in the amplitude of the waves.

How does the distance between the two loudspeakers affect the wavelength of the waves emitted?

The distance between the two loudspeakers affects the wavelength of the waves emitted in the sense that it can create either constructive or destructive interference. If the distance between the loudspeakers is an integer multiple of the wavelength, constructive interference occurs. On the other hand, if the distance is a half-integer multiple of the wavelength, destructive interference occurs.

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