Physics
Physics
Problem
A science teacher tells the class that a graph of displacement versus distance for a water wave shows several equally spaced peaks above and dips below the normal level of water. (i) Explain why the highest points on such a graph are called crests and the lowest points are called troughs. (ii) Describe, without using a diagram, the exact method you would follow to measure the wavelength and amplitude directly from this graph when a scale is provided along the horizontal and vertical axes. (iii) Sound waves travelling through air do not exhibit crests and troughs. Explain, with reason, which characteristic regions appear instead and why they cannot be located on the same type of displacement graph used for water waves.Intuitive explanation
The key to understanding this problem is recognizing that a displacement-versus-distance graph captures the spatial snapshot of a wave at one moment in time. Crests and troughs are simply the maximum and minimum displacements from equilibrium—the highest and lowest points the medium reaches. Wavelength and amplitude are geometric measurements you read directly from the graph's axes: amplitude is the vertical distance from the center line to a peak (or trough), while wavelength is the horizontal distance between two consecutive identical points (like peak to peak). Sound waves are longitudinal—particles oscillate back and forth along the direction of travel rather than perpendicular to it—so a displacement graph shows compressions and rarefactions as regions of varying density, not as visible peaks and troughs, making them impossible to pinpoint on a simple displacement-distance plot.
Intuitive explanation
The key to understanding this problem is recognizing that a displacement-versus-distance graph captures the spatial snapshot of a wave at one moment in time. Crests and troughs are simply the maximum and minimum displacements from equilibrium—the highest and lowest points the medium reaches. Wavelength and amplitude are geometric measurements you read directly from the graph's axes: amplitude is the vertical distance from the center line to a peak (or trough), while wavelength is the horizontal distance between two consecutive identical points (like peak to peak). Sound waves are longitudinal—particles oscillate back and forth along the direction of travel rather than perpendicular to it—so a displacement graph shows compressions and rarefactions as regions of varying density, not as visible peaks and troughs, making them impossible to pinpoint on a simple displacement-distance plot.