Two speakers send out sound in phase at a frequency of 779 Hz. When you are the same distance from both speakers you hear a maximum sound. Moving around, you hear essentially no sound when you are 65 cm from one and 85 cm from the other, and again when you are 123 cm from one and 183 cm from the other. What is the speed of sound here?

85-65 = 20 = half a wavelength

183 - 123 = 60 = 1 1/2 wavelengths natch ;)
so wavelength = 40 cm = 0.40 meters
period = 1/779 seconds
so
speed = distance/time = .4 *779 = 311.6 m/s

awful cold there

or high...

To find the speed of sound, we need to use the principle of interference. When two sound waves from the two speakers are in phase, they constructively interfere with each other and produce a maximum sound. When the waves are out of phase, they destructively interfere and cancel each other out, resulting in no sound.

Let's analyze the given information to figure out the speed of sound. We are given the frequency of the sound, which is 779 Hz. We are also given two sets of distances from the speakers, where we hear no sound.

First, let's consider the scenario where you are 65 cm from one speaker and 85 cm from the other. In this case, the difference in the distances from the two speakers is 85 cm - 65 cm = 20 cm. To have no sound, a path difference of λ/2 should occur, where λ is the wavelength.

Using the formula for the wavelength of sound, λ = v/f, where v is the speed of sound and f is the frequency, we can express the path difference in terms of the wavelength:

20 cm = λ/2

Next, let's analyze the scenario where you are 123 cm from one speaker and 183 cm from the other. Again, the difference in distances is 183 cm - 123 cm = 60 cm. This time, however, the path difference should be an integer multiple of the wavelength to produce no sound.

60 cm = m * λ, where m is an integer representing the number of wavelengths.

Now we have two equations:

20 cm = λ/2
60 cm = m * λ

From the first equation, we can solve for the wavelength:

λ = 40 cm

Substituting this value into the second equation:

60 cm = m * 40 cm

Simplifying:

m = 60 cm / 40 cm = 1.5

Since m should be an integer, we conclude that m = 3. Therefore, we have three wavelengths between the speakers. The total distance between the speakers is 3 * λ, which is:

3 * 40 cm = 120 cm

The wavelength is related to the speed of sound and frequency by the formula λ = v/f. Rearranging this equation, we find:

v = f * λ

Substituting the given frequency, we have:

v = 779 Hz * 40 cm

To convert cm to meters, we divide by 100:

v = 779 Hz * 0.4 m = 311.6 m/s

Therefore, the speed of sound in this scenario is approximately 311.6 m/s.