The sinusoidal wave shown in the figure below is traveling in the positive x-direction and has a frequency of 48.5 Hz.A sinusoidal wave is plotted on a coordinate plane. The wave is vertically centered on the horizontal axis. The vertical distance between a crest and a trough is 8.26 cm, and the horizontal distance between a crest and the nearest trough is 5.20 cm.(a) Find the amplitude. cm(b) Find the wavelength. cm(c) Find the period. s(d) Find the speed of the wave. m/s
Question
The sinusoidal wave shown in the figure below is traveling in the positive x-direction and has a frequency of 48.5 Hz.A sinusoidal wave is plotted on a coordinate plane. The wave is vertically centered on the horizontal axis. The vertical distance between a crest and a trough is 8.26 cm, and the horizontal distance between a crest and the nearest trough is 5.20 cm.(a) Find the amplitude. cm(b) Find the wavelength. cm(c) Find the period. s(d) Find the speed of the wave. m/s
Solution
(a) The amplitude of a wave is the maximum displacement from its equilibrium position. In this case, it is half the vertical distance between a crest and a trough. So, the amplitude is 8.26 cm / 2 = 4.13 cm.
(b) The wavelength of a wave is the horizontal distance between two consecutive crests or troughs. In this case, it is twice the distance between a crest and the nearest trough. So, the wavelength is 5.20 cm * 2 = 10.40 cm.
(c) The period of a wave is the time it takes for one complete cycle of the wave to pass a given point. It is the reciprocal of the frequency. So, the period is 1 / 48.5 Hz = 0.0206 seconds.
(d) The speed of a wave is the product of its wavelength and frequency. However, the wavelength should be in meters for the units to work out. So, first convert the wavelength from cm to m: 10.40 cm = 0.104 m. Then, the speed is 0.104 m * 48.5 Hz = 5.04 m/s.
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