Final answer:
To calculate the wavelength of a stationary sound wave when the distance between the first and the sixth node is known (30 cm), we use the relation that five half-wavelengths fit between these nodes. By performing the calculations, we find the wavelength to be 12 cm.
Step-by-step explanation:
To find the wavelength of a stationary sound wave when the distance between the first and the 6th node is given, we need to understand the concept of standing waves and nodes in Physics. A node is a point along a standing wave where the wave has minimum amplitude. In the case of stationary waves, such as those on a string or in an air column, the distance between successive nodes is half a wavelength (λ/2). Therefore, five half-wavelengths are between the first and sixth nodes (λ/2 × 5). Given the total distance between these nodes is 30 cm, we can calculate the wavelength (&lambda) of the sound wave.
To find the wavelength:
Find the value of five half-wavelengths: Distance between the 1st and 6th node = &lambda/2 × 5.
Therefore, 5 × &lambda/2 = 30 cm.
To find the full wavelength, &lambda, we rearrange the equation: &lambda = (30 cm) / 5 × 2.
Calculate &lambda = 12 cm.
Thus, the wavelength of the sound wave is 12 cm.