The displacement from the equilibrium caused by a wave on a string is given by: y(x, t) = (-0.00200 m) sin [40 m-1)x – (800 s-1)t]. What are the number of waves in 1 m
The number 40 in the sin(40x -800t) term is 2 pi/(wavelength).
Hence (2 pi) = (wavelength)*40 m^-1
wavelength = 2 pi/40 = 0.157 m
In one meter there are 1/0.157 = 6.4 waves
The amplitude doesn't affect the answer.l
To determine the number of waves in 1 meter, you need to find the distance traveled by one complete wave. In this case, a complete wave can be defined as one full cycle of the sinusoidal function y(x, t).
The general equation for a sinusoidal wave in the form y(x, t) = A sin(kx - ωt) represents a wave with amplitude A, wave number k, angular frequency ω, position x, and time t.
Comparing this equation with the given equation y(x, t) = (-0.00200 m) sin [40 m-1)x – (800 s-1)t], we can extract the values of k and ω:
Wave number, k = 40 m^(-1)
Angular frequency, ω = 800 s^(-1)
The wave number k represents the number of complete wavelengths (or waves) in one unit of spatial distance. Therefore, the number of waves in 1 meter is equal to 1/k.
Let's calculate it:
Number of waves in 1 meter = 1 / (40 m^(-1))
= (1 m) / (40 m)
= 0.025 waves
Therefore, there are 0.025 waves in 1 meter.