The equation of a transverse wave travelling along a string is given by "y=5 sin π (0.5x-40t)".
Find the:
a.Amplitude
b.Wavelength
c.Frequency
d.Velocity
e.Period
So what is your analysis?
To find the amplitude, wavelength, frequency, velocity, and period of a transverse wave given its equation, we can analyze the given equation step by step.
The equation of the transverse wave is given by:
y = 5 sin π (0.5x - 40t)
a. Amplitude:
The amplitude (A) of a wave represents the maximum displacement or height of the wave. In this case, the amplitude can be identified as the coefficient in front of the sine term, which is 5. Therefore, the amplitude of this wave is 5.
b. Wavelength:
The wavelength (λ) of a wave refers to the distance between two consecutive wave crests or troughs. In this equation, the term inside the sine function represents the argument, which is (0.5x - 40t). To find the wavelength, we need to isolate the x term.
0.5x - 40t = 0
0.5x = 40t
x = 80t
From the equation x = 80t, we can see that the position x changes linearly with time t. This implies that the wave is traveling with a constant velocity, and the wavelength is related to the velocity by the formula: wavelength (λ) = velocity (v) * period (T), where T is the period of the wave.
c. Frequency:
The frequency (f) of a wave measures the number of complete oscillations the wave makes in one second. To find the frequency, we can use the formula: frequency (f) = 1 / period (T).
d. Velocity:
The velocity (v) of a wave is given by the product of its frequency (f) and wavelength (λ): velocity (v) = frequency (f) * wavelength (λ).
e. Period:
The period (T) of a wave is the time it takes for one complete oscillation or cycle to occur. It is the reciprocal of the frequency, so period (T) = 1 / frequency (f).
By analyzing the given equation, we can conclude that the amplitude is 5. To find the wavelength, frequency, velocity, and period, we need to isolate the x term and analyze the relationship between x, t, velocity, frequency, and period.