Wave Motion

Wavelength is the spatial distance between two consecutive points in the same phase, such as crest-to-crest or trough-to-trough. It represents one complete cycle of the wave and is typically measured in meters.

The statement is false because it has the shifts reversed. Objects approaching the observer produce blueshift (higher frequency), while receding objects produce redshift (lower frequency).

Tsunamis travel at approximately 720 km/h (about 200 m/s or 400-500 mph) in deep ocean water, making option A correct. This high speed is why tsunamis can cross entire oceans quickly, though they slow down and gain height in shallow water near coastlines.

Wave speed is calculated as the product of frequency and wavelength: v = fλ. Option D correctly shows this relationship where the symbol represents wavelength. Options A and C incorrectly divide by wavelength, and option B has the correct factors but unclear notation.

When producing a wave on a spring, the wave velocity is determined by the medium's properties (tension, linear density, stiffness). You can change amplitude (how hard you shake), frequency (how fast you shake), and wavelength (resulting from frequency), but not the velocity itself; it's fixed by the spring.

Frequency is defined as the number of complete wave cycles (or crests) that pass a fixed point per unit time. By counting how many crests pass in a given time interval and dividing by that time, you directly calculate frequency. Wavelength (A) is the distance between crests, amplitude (B) is wave height, and velocity (C) is speed - none of these are calculated by counting crests over time.

Water waves are actually surface waves with both transverse and longitudinal motion - particles move in circular/elliptical paths rather than just up-and-down. However, the surface appears to move transversely (up and down), which is why this is often simplified as transverse in basic physics. Pure transverse waves have particles moving perpendicular to wave direction only, and pure longitudinal (like sound) have parallel motion.

Water waves are primarily transverse waves, where water particles move up and down (perpendicular to wave direction) as the wave energy travels horizontally. While water waves have some longitudinal components, they are classified as transverse.

Time for one oscillation is T = 2pi/12w = pi/6w,  so that the frequency = 1/T = 6w/pi Hz = number of oscillations each second.

Amplitude is the maximum displacement of a wave from its equilibrium position and represents the wave's energy or intensity. It is independent of other wave properties because you can change the amplitude without affecting frequency, wavelength, or velocity. Frequency and wavelength are inversely related through the wave equation, while velocity depends on the medium's properties.

The wave motion in which particles of the medium vibrate about their mean position in the same direction as the wave travels is called longitudinal.

y = a sin ( ωt + kx + π / 2) = a cos (ωt + kx).