Question

Two loudspeakers in a plane, 5 m apart, are playing the same frequency. If you stand 12 m in front of the plane of the speakers, centered between them, you hear a sound of maximum intensity. As you walk parallel to the plane of the speakers, staying 12 m in front of them, you first hear a minimum of sound intensity when you are directly in front of one of the speakers. What is the frequency of the sound? Assume a sound speed of 340 m/s?

Answer 1

The frequency of the sound is 68 Hz.

Step-by-step explanation:

To determine the frequency of the sound, we can use the concept of interference. When you stand 12 m in front of the plane of the speakers, centered between them, you hear a sound of maximum intensity, which occurs when the waves from both speakers are in phase and constructively interfere. This means that the distance traveled by the sound waves from both speakers to the point where you are standing is equal to a whole number of wavelengths. In this case, the path difference between the two speakers is equal to a whole number of wavelengths. The formula for constructive interference is given by:

Path difference = m * λ

Where m is an integer representing the number of wavelengths, and λ is the wavelength of the sound wave.

Since the path difference between the two speakers is equal to a whole number of wavelengths, we can write:

5 m = m * λ

Where λ is the wavelength of the sound wave.

Solving for λ, we get:

λ = 5 m / m

Substituting in the given values, we find:

λ = 5 m / 1

λ = 5 m

Now, we can calculate the frequency of the sound wave using the formula:

v = f * λ

Where v is the speed of sound and f is the frequency of the sound wave.

Substituting in the given values, we have:

340 m/s = f * 5 m

Solving for f, we get:

f = 340 m/s / 5 m

f = 68 Hz

Therefore, the frequency of the sound is 68 Hz.