Two waves are travelling on a string in the same direction. Both have a frequency of 101 Hz, a wavelength of 0.400 m, and an amplitude of 0.410 m. What is the amplitude of the resultant wave if the original waves differ in phase by π/4 rad?
Hey there,
Did anyone give you an answer? I'm just wondering because I too have a similar question.
boop on your woop
To find the amplitude of the resultant wave, we can use the concept of superposition. When two waves with the same frequency and wavelength travel in the same direction, the amplitudes of the waves add up to give the amplitude of the resultant wave.
In this case, the two waves have the same frequency (101 Hz), wavelength (0.400 m), and amplitude (0.410 m). The only difference is the phase shift of π/4 rad.
To find the amplitude of the resultant wave, we can use the concept of vector addition. Since the waves are in the same direction, their amplitudes can simply be added algebraically. The resultant amplitude is given by:
Amplitude_resultant = Amplitude_wave1 + Amplitude_wave2
Let's calculate it.
Amplitude_resultant = 0.410 m + 0.410 m
Amplitude_resultant = 0.820 m
Therefore, the amplitude of the resultant wave is 0.820 m.