Finding frequency and max speed from y = 6.1 sin(0.010x + 3.0t)

[mr_coffee]

Hello everyone! I got some parts of this question right but are stuck on others. Here is the problem:
The equation of a transverse wave traveling along a very long string is given by y = 6.1 sin(0.010x + 3.0t), where x and y are expressed in centimeters and t is in seconds. Determine the following values.

(a) the amplitude
6.1
(b) the wavelength
200
(c) the frequency
?
(d) the speed
?cm/s
(e) the direction of propagation of the wave
+x
[-x]
+y
-y

(f) the maximum transverse speed of a particle in the string
cm/s

From the equation i got the amplitude, From the wave # i got the wave length.
K = wave #
K = 2*pi/WaveLength
WaveLength=200

but now I'm stuck on how I'm suppose to find the frequency?
If i could find the period, i could find the frequency. or if i could find the angular frequency I also could find the frequnecy. Once I find frequency, finding speed would be easy. V = WaveLength*frequncey

How do you know the propagation of the wave? I got it right but it was through guessing.
-x was the answer.

Also how would i find the max speed? Does it invovle me taking the derivative of the function?

Thanks!

 

[nrqed]

Hello everyone! I got some parts of this question right but are stuck on others. Here is the problem:
The equation of a transverse wave traveling along a very long string is given by y = 6.1 sin(0.010x + 3.0t), where x and y are expressed in centimeters and t is in seconds. Determine the following values.

(a) the amplitude
6.1
(b) the wavelength
200
(c) the frequency
?
(d) the speed
?cm/s
(e) the direction of propagation of the wave
+x
[-x]
+y
-y

(f) the maximum transverse speed of a particle in the string
cm/s

From the equation i got the amplitude, From the wave # i got the wave length.
K = wave #
K = 2*pi/WaveLength
WaveLength=200

but now I'm stuck on how I'm suppose to find the frequency?
If i could find the period, i could find the frequency. or if i could find the angular frequency I also could find the frequnecy. Once I find frequency, finding speed would be easy. V = WaveLength*frequncey

How do you know the propagation of the wave? I got it right but it was through guessing.
-x was the answer.

Also how would i find the max speed? Does it invovle me taking the derivative of the function?

Thanks!

The angular frequency $\omega$ is simply what multiplies the time ! (so 3.0).

A traveling wave moves to the right if the x and t terms have opposite signs.

You could find the velocity by taking the derivative with respect to time and then find when the velocity is max, but the quick answer is that the max speed of a particle is $A \omega$

Patrick

 

[mr_coffee]

THanks a lot man! WOrked perfectly!

 

[lightgrav]

What makes you think that the wavelength is 200 [cm?]?
k is the quantity that multiplies x , so wavelength = 2 pi /.01 = 628.

 

[nrqed]

What makes you think that the wavelength is 200 [cm?]?
k is the quantity that multiplies x , so wavelength = 2 pi /.01 = 628.

Good point, lightgrav... I did not check the parts that he said he had no problems with. He forgot the factor of pi.

Pat