A sinusoidal transverse wave traveling on a string is described at t=2.0s by y(x)=0.1sin(4πx+(33π/40) and at x=1.0m by y(t)=0.1sin((17π/4)+4πt)
a. What is the wavelength and the amplitude?
b. What is the frequency (Hz) and direction of propagation?
c. What is the speed?
d. Write down the full equation for displacement at position x and time t
e. Describe a wave whose simultaneous presence in the string would create a standing wave
The Attempt at a Solution
Amplitude= 0.1 m
Wavelength- I know the wavelength is a measurement of the distance between two identical points aka the distance for one cycle to occur; however, I'm not sure if this means that the wavelength here is just 4π or if it should be something like 4π/2, which references the distance of one rotation.
Frequency- I know frequency should use the second equation, which is a function of time. Can I just do 2πf=17π/4 and solve for f? That gives me 8.5 Hz. From here I know I can find the speed, but I'm not sure if these calculation are correct.