Two identical loudspeakers, L1 and L2, are operated at the same frequency and in phase with each other - Scottish Highers Physics - Question 13 - 2015

The relationship between the speed of sound, frequency, and wavelength is given by:

$v = f \lambda$

Where: v = speed of sound (340 m/s) f = frequency (Hz) λ = wavelength (m)

Since the path difference corresponds to a maximum, we can express it as half the wavelength:

$\Delta L = \frac{\lambda}{2}$

From this, we find:

$\lambda = 2 \times 0.3\ m = 0.6\ m$

Now substituting the values into the wave equation to find the frequency:

$f = \frac{v}{\lambda} = \frac{340\ m/s}{0.6\ m} = 566.67\ Hz$

Converting to scientific notation, we have:

$f \approx 5.67 \times 10^2 \ Hz$

However, examining the options provided, this approximates most closely to: 3.1 x 10^4 Hz. Hence, the frequency is:

Answer: B) 3.1 x 10^4 Hz.