Final answer:
By using the relationship between phase difference, wavelength, and distance, and knowing the frequency of the sound and the speed of sound, we can calculate the phase difference results in a distance of approximately 2.22 meters between the two points on the x-axis.
Step-by-step explanation:
To calculate the distance between two points with a given phase difference when a sound is emitted, we use the relationship between phase difference, wavelength, and distance. Since the loudspeaker emits a tone at 130 Hz and the speed of sound is 340 m/s, we can first calculate the wavelength using the formula λ = v/f, where λ is the wavelength, v is the speed of sound, and f is the frequency. Substituting the given values, we get λ = 340 m/s ÷ 130 Hz, which gives us a wavelength of approximately 2.615 m.
To find the distance (Δx) corresponding to the phase difference (Δφ) of 5.4 rad, we can use the formula Δφ = (2π÷Δx)/λ. Rearranging for Δx, we have Δx = (Δφ×λ)/(2π). Plugging the numbers in, Δx = (5.4 rad × 2.615 m)/(2π), which yields a distance of approximately 2.22 m between the two points on the x-axis with the specified phase difference.