A sinusoidal wave travels along a string. The time for a particle to move from maximum displacement to zero is 0.170s. What are the a)period b)frequency c) the wavelength is 1.40m what is the wave speed?
ok I know i need the equation T=1/f and the wave equation
y=YSIN{kx-wt} --> wavenumber and angular frequency
so
k= 2pi/lambda w= 2pi/T
so I know the time is 0.170s. I am confused as how to find T. They do not give me the amplitude or w inorder to find T. If you could explain to me how to find it I could do the rest of the problem I think.
Thank you
OK, time for one fourth cycle is .170
Period= 4 times that
freq= 1/ period
frequency*wavelength= speed
To find the period (T), we can use the information given that the time for a particle to move from maximum displacement to zero is 0.170s. We know that this time represents one-fourth of a cycle. Therefore, the period (T) is four times this time:
T = 4 * 0.170s
T = 0.680s
Now, we can find the frequency (f) using the equation:
f = 1 / T
Substituting the value of T we just found:
f = 1 / 0.680s
f ≈ 1.47 Hz
Next, we can determine the wave speed by multiplying the frequency (f) by the wavelength (λ):
wave speed = frequency * wavelength
Given that the wavelength (λ) is 1.40m and the frequency (f) is approximately 1.47 Hz:
wave speed ≈ 1.47 Hz * 1.40m
wave speed ≈ 2.05 m/s
So, to summarize the answers:
a) The period (T) is 0.680s.
b) The frequency (f) is approximately 1.47 Hz.
c) The wave speed is approximately 2.05 m/s.