Two loudspeakers emit sound waves along the x-axis. The sound has maximum intensity when the speakers are 35.9cm apart. The sound intensity decreases as the distance between the speakers is increased, reaching zero at a separation of 109.1cm. What is the wavelength of the sound?
b). If the distance between the speakers continues to increase, at what separation will the sound intensity again be a maximum?
To find the wavelength of the sound, we need to use the concept of interference between the sound waves from the two loudspeakers.
First, we can calculate the distance between two consecutive maximum intensity points. This distance is equal to half the wavelength of the sound. Let's call it λ/2.
Given that the sound has maximum intensity when the speakers are 35.9 cm apart, and reaches zero intensity at a separation of 109.1 cm, we can calculate the distance between two consecutive maximum intensity points by subtracting the two distances.
λ/2 = 109.1 cm - 35.9 cm
Simplifying,
λ/2 = 73.2 cm
To find the wavelength (λ), we just need to double this value.
λ = 2 * 73.2 cm
λ = 146.4 cm
Therefore, the wavelength of the sound is 146.4 cm.
b) To determine at what separation the sound intensity will be a maximum again, we need to consider that the maximum intensity occurs when the path difference between the two sound waves from the speakers is equal to an integer multiple of the wavelength.
In this case, since the separation between the speakers is continuously increasing, the separation for the next maximum intensity point will be when the path difference is equal to one wavelength.
Therefore, we can calculate the separation by adding one wavelength to the initial separation when the sound had maximum intensity.
Separation for next maximum = 35.9 cm + λ
Substituting the calculated value of λ,
Separation for next maximum = 35.9 cm + 146.4 cm
Separation for next maximum = 182.3 cm
Therefore, if the distance between the speakers continues to increase, the sound intensity will be maximum again when the separation is 182.3 cm.