Question

Which of the following wave(s) can produce standing wave when superimposed with \[y = A\sin (\omega t + kx)\]:
A) \[A\sin (\omega t - kx + {30^0})\]
B) \[A\cos (\omega t - kx)\]
C) \[A\sin (kx - \omega t)\]
D) None of these

Answer 1

Hint:A wave that oscillates in time, but the pinnacle amplitude profile does not shift in place is a standing wave in physics, also known as an intermediate wave.

Complete Step by Step Solution:
If two or more waves hit the same point, they overtake each other. In fact, as they come together, wave disturbances are superimposed – a process called superposition. Each perturbation is a force and power adds. The resulting wave, if the disturbances are along the same lines, is a single addition to each wave's perturbations — their amplitudes are applied.

While pure constructional and pure destructive interference occurs, similar waves are precisely matched. A mixture of positive and disruptive interference may be generated by the over position of most waves and varies from place to place. For e.g., sound from a stereo may be noisy at one location and silent at another. Different loudness ensures the sound waves are added in different places partly and destructively. A stereo has at least two speakers, which produce sound waves. Superimpose all these waves. The blended whine of aircraft jets detected by a stationary passenger is an example of noises that range from constructive too disruptive over time. The combined sound will fluctuate in frequency as the sound of the two motors ranges from positive too disruptive in time.

For standing waves to be formed the interfering waves must have the same amplitude, same frequency and opposite direction of travelling. These are satisfied by options A and B.

Note:A closer glance at earthquakes reveals that resonance, permanent waves and constructive and disruptive interference exist. A building will vibrate for a couple of seconds with a driving frequency that fits the normal vibratory frequency, resulting in a resonance that collapses one building as adjacent buildings fail. Houses of a certain height are always devastated when others are untouched. The height of the building is ideal for setting up a wave for this precise height.