A sonar signal of frequency 1.00 106 Hz has a wavelength of 1.40 mm in water.
(a) What is the speed of the signal in water?
(b) What is its period in water?
(c) What is its period in air?
To answer these questions, we can use the wave equation formula, which relates the speed (v), frequency (f), and wavelength (λ) of a wave.
1. Speed of the signal in water (v):
The wave equation formula is v = f * λ. Since the frequency (f) is given as 1.00 * 10^6 Hz and the wavelength (λ) is given as 1.40 mm (which can be converted to meters as 1.40 * 10^-3 m), we can substitute these values into the formula:
v = (1.00 * 10^6 Hz) * (1.40 * 10^-3 m)
v ≈ 1.40 * 10^3 m/s
So, the speed of the signal in water is approximately 1.40 * 10^3 m/s.
2. Period of the signal in water (T):
The period (T) of a wave is the time it takes for one complete cycle. It can be calculated by taking the reciprocal of the frequency (T = 1/f). Using the given frequency of 1.00 * 10^6 Hz:
T = 1 / (1.00 * 10^6 Hz)
T = 1.00 * 10^-6 s
So, the period of the signal in water is 1.00 * 10^-6 s.
3. Period of the signal in air (T):
The period of the signal remains the same, regardless of the medium it is in. Therefore, the period of the signal in air will also be 1.00 * 10^-6 s.